A classic road lever has a free to pivot fitting with a stepped hole, and usually a slot to make cable installation easier by sliding in from the side. It's absolutely critical that the cable head is of the right type, and fully pocketed into the fitting. If not, cable tension will rotate the fitting and dump the head out the side.

I suggest you thread the cable and pull on it to test it's stability, and only finish attaching it when you're 100% sure it's seated and won't pop out. Also be aware that if the fitting is a bit sloppy, the cable can sometimes unseat when slack as you thread the rest of the run, so recheck it before tightening the pinch bolt.

I also have a lever where the wire can unseat when slack. I prevent it by jamming a small balled wad of paper behind it to keep it in place while I work, then remove the ball when finished.