Your 95 dodge neon stop running while you were driving with no warning just the check engine light came on the it stop?
You need to find out what the check engine light came on for. Have the computer scanned for codes. When certain errors occur that could damage the engine, sometimes the computer will just shut down the engine to prevent damage. That may be what happened to you.
What will cause the engine to stop running while driving and the check engine light does not come on when engine stops running?
No. Check engine lights do not immobilize cars. But the light may be warning you of a problem that your car has that may be stopping it from running. FYI: Check engine lights come on for all sorts of problems, from a loose gas cap to an engine that has been completely destroyed. Regardless of what you might think that is causing the light, you should safely get your car to a certified auto-mechanic.