They can die of any cause even if not part of the active family, though it's difficult to actually kill them off. Emotional deaths are easiest to induce through cheating, if you're willing to do that; you can shift-click with debugging commands enabled and manually set them into a deadly emotional state. (I don't know how to enable debugging commands without MC Command Center, though; many of the debugging commands (including this one) are hidden even with testingcheats enabled.)
If you want to kill them without cheating, the easiest way would probably be to invite them over and lock them in a room. Now you have two options. The passive way, which requires the least effort, is to just leave them there until they starve. The other, more sadistic option, is to kill them by embarrassment. Make sure the victim is locked in a room with a shower but no toilet, and make sure the door is locked so your Sim can freely enter and leave but your victim can't. Have your Sim hang around in there with the victim until they pee themselves, at which point they will become Very Embarrassed (having a coffee maker in the room may speed this up, since the victim may autonomously drink the coffee). Now, have your Sim leave. The victim, whose hygiene need has now been completely depleted, will take a shower to clean themselves up after their little "accident". Have your Sim enter the room again while the victim is showering, and they will now become Mortified and potentially die of Embarrassment. If you're feeling particularly evil, you can have your Sim stick around at this point and keep up conversation with the victim, doing their best to keep the conversation as awkward as possible until they drop dead, though this isn't necessary.
