If the currency ceased to exist upon death then that would make killing for it less enticing to criminals. Once you pay someone for something and transfer some of your currency it becomes theirs so it would not disappear. Yet what you have at the time of death could disappear. I know some people may not like that idea because they cannot pass it onto their children. However, for it to truly work each person must only have their own currency and what was given to them in voluntary trade by another.
When you die your currency income ceases. Thus, if you promise future currency there is no future currency beyond your death. Again that actually might discourage killing.
EDIT: Unlike "In Time" I am proposing that currency be the same for anyone. It is accumulated as time passes. You cannot collect for time that has not yet passed. If you die suddenly then your currency stops then as well.
It would be very different from what we are used to. Yet that doesn't mean it might not be feasible.
RE: What do you think about a currency backed by time?