April 30, 201015 yr (S)he dies. Shinigamis aren't supposed to kill someone if it wasn't their time. (S)he does to keep Misa safe. In return though, since (s)he did what no shinigami should do, (s)he dissolves into ash (or whatever it is). I believe (s)he goes to nothingness.
In Deathnote after Rem kills L
where did she go