What we know:
Subsuming (Sacrificing) a warframe to gain its ability takes 24h, and requires resources gained from Helminth in exchange for old resources, destroying the warframe entirely.
Each warframe will have a single ability granted from doing so.
The resulting ability will not be a 4th slot ability, or a signature ability (Ivara's Quiver, Loki's Invisibility, Wisp's Reservoir, Nezha's ring, etc.)
Prime warframe can be augmented with the swappable abilities, but cannot be sacrificed.
Any warframe can equip the ability once unlocked, replacing any of their 4 abilities regardless of what slot the original ability occupied.
Only one swapped ability per warframe, though the swapped ability may be confined to specific mod configurations.
Ranking up the Helminth system Intrinsics style by utilizing the system grants new abilities designed by Helminth himself.
Without further ado...
Ash: Shuriken. Augment: Seeking Shuriken.
As you'll notice with many of the frames on this list, the most likely candidate is the first ability. Ash's Shuriken has a useful augment for armor stripping, so this option may be viable for many builds or warframes that struggle with enemy armor.
Atlas: Tectonics. Augment: Tectonic Fracture.
As much as I would like for Landslide to be Atlas' subsumed ability, I am afraid that with the added mechanic of it granting Rubble, DE won't make it so. I would like to be wrong here, but Tectonics does have its uses. One example is the Index, blocking AI from dropping off points, and Free roam missions for protecting objectives. May be useful for solo players in such cases.
Banshee: Sonic Boom. Augment: Sonic Fracture.
Like Ash, Banshee has a useful first ability with an armor stripping augment. Unlike Shuriken, it is shorter ranged, but area of effect in a cone and has added CC in the form of a knockdown/ragdoll.
Baruuk: Lull. Augment: Endless Lullaby.
Some may think that Elude is a more likely candidate, but much like Atlas' Landslide, Elude has a secondary mechanic specific to the warframe. However, Lull is notorious among Intrinsic and Focus farming as a powerful stealth-kill affinity multiplying ability, and is even useful as CC in general. This may be a powerful addition to any warframe that lacks for CC, or has powerful AoE abilities that will make farming EXP much simpler.
Chroma: Vex Armor. Augment: Vexing Retaliation.
Here we have the first 3rd slot ability on the list, and may be a bit of a stretch. Vex Armor is a powerful ability that will benefit many frames - especially frames lacking in shields. It is a combination of defense and offense that many frames will desire. However, the alternative is Spectral Scream - a much less useful ability. The reason I do not believe Spectral Scream is because it uses Chroma's color system to determine the element, but I could very well be wrong here.
Ember: Fireball. Augment: Fireball Frenzy.
Fireball gives a warframe a reliable way to proc Heat status, while doing moderate damage for a swapped ability. Better still, with the augment a warframe is capable of adding an additional element to their weapon, as well as boosting its damage by percentage. Great support augment for boosting the whole team, and if combined with other elemental buffs on this list, we may see some interesting combined elements becoming meta. Also useful for Profit Taker runs, as another free element grants much more freedom for speed runs.
Equinox: Metamorphosis. Augment: Duality.
Equinox is a very special cookie. Either DE will divide one of their abilities - effectively halving its usefulness - or they will use Metamorphosis; a mediocre buffing ability that alternates between an armor bonus or a shield bonus. The augment, however, would allow players to create an autonomous clone of themself to aimbot enemies.
Excalibur: Radial Blind. Augment: Radiant Finish.
Some may believe Slash Dash is more likely. However, Slash Dash utilizes the Exalted Blade, which is unique to Excalibur. radial Blind allows a warframe to CC enemies with a blinding stun, while opening them to finishers. This is great for both crowds of enemies, as well as for ignoring the armor of a beefier target that may take longer to take down otherwise. This is because Finisher damage ignores armor. An alternative would be Radial Javelin, but I do not believe DE would make a starter warframe capable of subsuming a 3rd slot ability.
Frost: Freeze. Augment: Freeze Force.
Another useful first slot elemental ability. Freeze allows a warframe to completely immobilize an enemy, and the augment grants a radial weapon damage buff to allies in the form of cold element.
Gara: Spectrorage. Augment: Spectrosiphon.
Being a third slot ability, Spectrorage is the only one of Gara's abilities that qualify. Shattered Lash would qualify as a 'signature' ability, Mass Vitrify, an ultimate, and Splinter Storm physically utilizes Gara's glass armor, making it another signature ability. While not much more than a CC ability on its own, the augment causes enemies to drop energy orbs... however, the usefulness of this is negligible in regards to its high energy cost as a third slot ability.
Garuda: Bloodletting. Augment: Blood Forge.
Another 3rd slot ability, however, Bloodletting is unique in that it costs no energy, instead costing health to grant energy. Garuda's other abilities are mechanically bound to her warframe, so I find this the most likely candidate. It grants great utility to a plethora of frames - particularly frames with built-in healing abilities - and makes a great addition in many scenarios. The alternative here would be Blood Altar, granting any warframe a useful single-target hard CC that restores health to nearby allies.
Gauss: Thermal Sunder. Augment: N/a
The rest of Gauss' abilities utilize his unique mechanic - the battery - and are likely excluded. Still, this 3rd slot ability provides adequate AoE damage of multiple elements.
Grendel has NO applicable abilities, given the restrictions DE has revealed. Grendel's signature ability, Feast, fuels his other 3 abilities in their entirety. If I were to make a guess, they will provide a special version of Regurgitate; allowing the warframe to fire a toxic projectile at the cost of 25-75 energy rather than a consumed enemy.
Harrow: Penance. Augment: N/a
Some have mentioned that Condemn would be a powerful subsumed ability, but I fear it falls under the Signature ability restriction. However, Penance can be a powerful buffing ability that increases attack speed/fire rate for the warframe and their allies, as well as a 5% lifesteal healing aura.
Hildryn: Pillage. Augment: Blazing Pillage.
Alternatively, it could be Haven. However, I fear that Haven's high shield drain would prevent it from being useful on any frame that doesn't have 1k+ shields with Redirection equipped. Pillage's base shield cost of 150 is much more attainable, and provided a powerful shield/armor stripping ability to warframes.
Hydroid: Tempest Barrage. Augment: Corroding Barrage.
An RNG based AoE damage ability with an armor stripping augment. May be more useful for large groups of enemies, or on frames that need to utilize -range for their builds.
Inaros: Desiccation. Augment: Desiccation's Curse.
Powerful cone AoE blind ability that can be used to open an enemy to finishers, ignoring their armor. Also restores a small amount of health due to the leech of the DoT effect.
Ivara: Navigator. Augment: Piercing Navigator.
As Ivara's other abilities are signature, we are left with Navigator. This ability can be useful for eliminating priority targets, or buffing a single shot to kill a boss or similar. Not entirely powerful, but can be a fun skill to use.
Khora: Ensnare. Augment: N/a
A useful AoE CC ability that can be used to pull enemies close. May be devastating when combined with warframes with more powerful abilities lacking in AoE. without Whipcrack to refresh the duration and spread to additional groups, it may be best to use it in bursts.
Limbo: Banish. Augment: Rift Haven.
Limbo's abilities solely utilize enemies in the rift. With the given restrictions, only Banish meets the requirements. However, if you thought Limbo was a troll before, imagine any warframe banishing an enemy while having no way to extend any player's reach into the rift. We'll see what happens here.
Loki: Decoy. Augment: Savior Decoy.
A player should not discredit the usefulness of a good, well-placed decoy. This is made all the better with the augment adding an additional layer of protection. Given that Decoy's stats are based on the stats of the warframe, we may find some particularly tanky combinations.
Mag: Pull. Augment: Greedy Pull.
I personally find that Ragdolling enemies is counterproductive much of the time, but the Greedy Pull augment may be useful for energy-starved frames, or builds that need lots of ammo.
Mesa: Ballistic Battery. Augment: Ballistic Bullseye.
An underwhelming ability, though the augment may be useful in increasing status chance.
Mirage: Sleight of Hand. Augment: Explosive Legerdemain.
Not the ability one would want from this bounty of useful tools, but the only one that meets the criteria. May have some use on Corpus missions, but largely underwhelming.
Nekros: Soul Punch. Augment: Soul Survivor.
An augment that allies instant revives. Largely lackluster. Alternatively, we may get terrify, which would be useful for CC and armor reduction, at the cost of being a 75 energy cost ability.
Nezha: Fire Walker. Augment: Pyroclastic Flow.
Excellent speed-boosting ability with moderate CC and heat procs to strip armor. Most likely candidate, as other abilities use Nezha's signature Chakram Ring to be used.
Nidus: Larva. Augment: Larva Burst.
Great CC ability that pulls and ragdolls enemies in a targeted location. With a max range buffing warframe, this could be used to eliminate groups of enemies using melee. Alternative is Virulence, though I doubt its qualification due to the stacking mechanic.
Nova: Null Star. Augment: Neutron Star.
A buff that reduces damage taken, though on frames that need range this may prove less useful, as the stars will seek out targets rather than mitigating damage.
Nyx: Psychic Bolts. Augment: Pacifying Bolts.
A powerful, one-handed armor-stripping ability.
Oberon: Smite. Augment: Smite Infusion.
Oberon's Smite is useful for CC, damage and with the augment can be used to grant increased weapon damage in the form of Radiation. This makes it very useful for combating Grineer, Eidolons or even grouping with other Element-based weapon buffs.
Protea: Blaze Artillery. Augment: N/a
A simple damage ability capable of stacking high damage multiplier against multiple enemies.
Revenant: Reave. Augment: Blinding Reave.
Alternatively, Mesmer Skin. However, I fear it falls under the Signature category do to the free thrall effect. Sadly, this ability sees a diminished effect due to the inability to Thrall targets. Otherwise, it can be a great tool for stealing health and shields.
Rhino: Rhino Charge. Augment: Ironclad Charge.
A short dashing attack that can be used to ragdoll enemies. Augment may be useful for frames that utilize armor. Some may think Roar is likely, but I fear it falls under Signature restriction both because of its use, as well as the presence of Rhino's 'voice' in the use.
Saryn: Toxic Lash. Augment: Contagion Cloud.
Alternative is Molt, though I feel it uses Saryn's model and may count as a signature. Still, Toxic Lash is a wonderful weapon damage buff capable of greatly increasing damage for a time.
Titania: Spellbind. Augment: Spellbound Harvest.
Status immunity for team.
Trinity: Link. Augment: Abating Link.
A damage mitigation ability that can be used for armor stripping.
Valkyr: Paralysis. Augment: Prolonged Paralysis.
A low-cost ability granting an AoE stun with damage based on the warframe's shields. May be very powerful on Hildryn.
Vauban: Photon Strike. Augment: Photon Repeater.
Deployable AoE burst damage.
Volt: Shock. Augment: Shock Trooper.
Chaining elemental CC with a buffing support augment.
Wisp: Wil-O-Wisp. Augment: N/a
May be a useful mobility or distraction tool. Alternative: Breach Surge.
Wukong: Cloud Walker. Augment: Enveloping Cloud.
Useful for healing a warframe, as well as good mobility skill.
Zephyr: Airburst. Augment: N/a
Projectile burst AoE that ragdolls.
Think I made a mistake? Thought of a powerful combination? Post it below!