Attention, coverage, starting conversations, etc. There really isn't much downside in faking this as far as I can tell, you get sympathy and coverage.
To be fair, it is probably likely that a good amount of this sort of thing is the work of button pushing internet trolls who get a thrill out of sending a direct message to a well known person that gets attention, but I'm saying I have no way of knowing if they are legit or not, they more often than not are not serious threats, and there is incentive to actually fake this.