That's not really a silly question, as many people are afraid of that. The answer is really simple though. It is absolutely impossible for that to happen, ever. That's something you don't have to worry about at all.

Your dreams take place during the phase of sleep called REM-sleep. Although there are techniques to prolong your dreams, you can no longer prolong them when your REM-sleep is over and you switch to a different sleep-phase. This means you can't possibly get stuck in a dream.

As for the dying thing: that's impossible as well. The way you wake up is because you were mentally stressed. After all, you were having a nightmare. All dreams, however, are really just thoughts, only they're more realistic. Dreams are pure fantasy. You're as likely to die in a dream as you are when you are fantasizing about something while awake. In fact, lucid dreaming is a very good way to get rid of these nightmares you're talking about, but that's a different subject.