I have been unable to determine exactly what the cause of this bug is but I do know that it only seems to occur when in the Undercroft as I have never seen the problem affect the Drifter.
If you have the Luscinia’s Suffering decree it is possible for its effect to affect you. The problem becomes stuck to your Warframe and will persist out of the Undercroft and will appear both in Duviri transference, re-entering the Undercroft and also in the final boss fight. Having the effect on you also seems to cause a problem with mounting the wild Kaithe that spawns in the second phase of the Steel Path version of the boss fight which then causes the Kaithe to despawn. You will quickly die and then respawn on a new Kaithe in the outer ring. Death as a Warframe seems to be the only way to clear the bug once it has manifested.
This has happened to me as well as to my son on multiple occasions both grouped up and solo.