I volunteered for a no-kill shelter back in college. Maybe not quite who you’re asking about, but at least close.
The animals we did put down were incredibly sick or injured, and usually in a lot of pain. Yes, it was sad that their previous owners let them get that bad, but there was a clear upside in that it really was merciful.
Left me hating humans even more than I did before, though. Fuck humans who consider pets as little more than decorations, they need to be put down.