Curses are very selfish at times.
Lets say you’re cursed to die in a month. You would think you’d be as mortal as anyone else, but you’ll be wrong. Because now they can’t die until the curse says so. It doesn’t matter how many times they step in front of traffic or what fights they get into, you’re effectively immortal; the curse will protect you until it kills you.
That’s my human, the curse thinks.* Killing them is my job.
This has several benefits. Sure, you’re gonna die, but you’ll know when. You’ll be able to get your affairs in order, plan your funeral, borrow a load of money, frame your enemies, whatever you want.
*Or it would if curses were sentient.