Rykon
Five Thousand Club
Just an additional suggestion, perhaps they have an item they are bound to. Some sort of treasure which can act as a gateway to a sanctum of a sort. Anytime their oath keeper perishes they retreat into their vessel waiting to be approached by the inheritors of their miraculous item. Whether that be a blood descendant of the previous master could be considered a trivial concern to some or a matter of great consternation to others. In the latter case they could demand proof of worthiness in some trial or another. Or if it's a particularly picky djinn, maybe all inheritors must pass their trial before agreeing to being bound in servitude.