You can earn an inheritance from anyone, it seems: the
WIKill03 script that drives the inheritance quest doesn't seem to have any conditions on it that restrict potential bequeathals to actors of specific factions, based on poking around in the scripts (
QF_WIKill03_001BFF2 as well as the base world interaction, quest and courier scripts). Your disposition with the deceased has to be high enough, otherwise the reward scales to zero and nothing will happen, but otherwise you can get inheritance letters delivered from random bandits, et cetera.
However, whether or not you actually ever get the award is gated by a bunch of complex factors relating to how often the quest can re-occur (the inheritance quest is on a ~40 day timer, if I recall correctly), what other potentially higher-priority quests were running, and so on. Most of those factors are rather difficult for you to control in any meaningful way, so you can't easily set up an on-demand payout from this question by killing somebody at any time you want.