Eventually, yes, your character will die if played long enough. As noted elsewhere, this is very rare on CF -- I'd say far less than 1% of characters disappear for any reason other than the player choosing to delete them.

Still, I understand that this seems a frightening prospect to people used to other kinds of MUDs or similar games. CF is a little different kind of game in ways that are hard for me to explain relating to this, but please try and trust me when I say it's really not a big deal. For the moment, try not to think about it and just have a good time.