could another user delete my facebook account?

[JaguarsNFLfan#1]

When ones go to block another user on facebook, a new option appears on their account reading:

This is my old profile
Recover this account, it's hacked
Close this account

If I select this is my old profile, close this account, what happens? Will the other user's account get closed.
Also, could somebody do that to delete my account, just to be mean?
Now I am worried somebody might try to delete my facebook account.

[Cierra Gallegos]

other user can only delete account if they have ur password but if they dont no they can not