What would happen if a pilot tried to escape a damaged fighter with only a parachute?

Answer 1

With modern jet powered fighter aircraft survival would be practically impossible as he would be struck by parts of the aircraft. An ejection seat is needed to ensure that he completely cleared the aircraft and was at a safe distance before deploying the parachute.

Older propeller driven fighter aircraft as used in WW2 and earlier escape was usually possible with just a parachute because of lower speeds, but pilots still had to be careful to avoid hitting the tail structures on some fighter aircraft.