If it leaves you at a better position than you were at previously, then I'd say yeah. It's not the same as going from the pan to the fire if you're now safe, even if you've become so radically indentured to your savior.
With the OP example what you have to debate is whether his new circumstance is better than being fucking dead, and since it was caused by the same people who killed him that's not saving him at all.

>>119945
Even the normal undead are utterly beholden to their resurrectors to survive. Their lives aren't their own at that point. Benevolent necromancers may allow them a great degree of freedom, but a freedom that can be taken away isn't a freedom. It's a luxury that distracts a slave from their position.

Maybe. Sounds pretty terrible to me. Sounds like a prolonged suffering thing, but OP is alluding to a specific situation from a specific anime and for that I'd say the answer is probably no.
I think in these situations there's usually some free time or small joy found since the human mind is capable of great feats of adaptation.

Only the dead can know peace from this evil.

Consider this scenario:
The one you're eternally indebted to is a cute girl

I think then we can consider that you have been saved.

>>119991
It seems it's actually in the WN that Shalltear takes a lot more prisoners, like Arche and Brain becoming her sex slaves. Maru decided to off them the second time around, and I'm very glad he did so.