Tridolon Host migration

[KamikazeKamanzi]

Tridolon hunting is quite notorious for host migrations but is there a way we can keep our brilliant eidolon shard (used to summon) if we are unexpectedly disconnected from the hunt or is that something that will lead to abuse of force quitting if a group were to fail at the hunt? And also I feel like when I do disconnect there is never an option to join back like there would normally be outside of PoE.