There may also be some difference between "naturally arising" undead and those that are purposely animated. For example, in the Viking Sourcebook from 2E, there were some undead who were fully themselves in their animation and may visit their family to announce their own deaths, or visit their enemies to avenge themselves.
At least a couple RPGs have "Speak with (the) Dead" spells. Last I checked, in D&D the corpse had to answer truthfully. The HARP version appears to let the corpse answer however it wants.
This does move us away from undead slaves vs. living slaves. So suppose you have a good/neutral necromancer whose buddies lost a nasty fight, yet somehow the necromancer survived. If the necro is a polite sort, I can see them asking their buddies through Speak with Dead "So, that really sucked, and I'm alone now. There's no way I can make it out alone. May I animate your corpses until I get out and we can get you a proper resurrection? Who knows, on the way out, maybe you can avenge yourselves?" Then the necro's dead buddies can answer however they want.
Depending on how soon soul departure happens in the given world, different complications can arise. Take the idea of Petitioners from 2e Planescape. "So, can I use your corpse to help me fight?" This can go many different ways. The most obvious of which is the necromancer having to convince the petitioner that they know each other. Once that's established, it can go many ways. But I'll take me personally: Let's imagine I'm dead, I'm in an afterlife and enjoying it. My living buddy calls me on a necro call and asks to use my corpse. "Why not, I'm never going to be using that body again."