If they became a heartless they would be dead anyway in a way.The body (nobody) is just a shell.It is not alive as such and if you can get me proof that a nobody is body and soul then I am wrong but unless you can provide that I will belive what I wrote.
Nobodies are born when a heart is swallowed by darkness and becomes a Heartless. They are the remaining parts left behind by the heart: the body, giving a Nobody form, and the soul, giving the Nobody life.
A Nobody is made up by the body and soul of their somebody