It's a *Remarkably* common thing for a DM, at the end of of dangerous encounter, as the last of the nasties drops, to say:
"We're not out of initiative yet... Player, you're up, what are you doing?"
Whenever anything time sensitive is going on, you stay in initiative - and the most common reason after a gruelling battle, is in the case of downed allies and whether they'll have to risk any more saves before someone can stabilise or heal them. This is a pretty normal staple of combat etiquette, and is something that should, as Larian have demonstrated to us very clearly, be carried over into video game format in some fashion.