Hello MTG rules enthusiasts!

I generally play multiplayer EDH, so I have learned that when a my opponent A reanimates my Eager Cadet with a Sepulchral Primordial, the Cadet would typically get exiled if he still controls it when he loses. What happens if I play a Act of Treason to gain control of my Cadet until end of turn, and bring my opponent A to zero life during that same turn? Does the Cadet still get exiled?

Thanks for the help.

I would assume that, as the controlling player, you get to keep it and it doesn't get exiled because it is owned by you and it can't go back to a board that isn't there.

Keep in mind I play about zero EDH and find many of its rules silly.

The rules for handling what happens when a player leaves a m game can be summarized in three principles:
(a) The leaving player must be able to scoop up everything that belongs to them and just walk out the door,
(b) Anything that doesn't belong to them that they were using shouldn't stay on the 'field, and
(c) Everything else can stay as it is.

Applying those three principles answers 96% of most questions about what should happen to things.

As to your specific scenario:

There's actually a rule that directly addresses this possibility:

Perfect, thanks! This was actually the possibility I had considered least likely, but there it is! So I'd get my Eager Cadet for the remainder of my turn, and then it would be exiled in the cleanup step.

Thanks for the help!