If you stay in a disadvantaged position for too long, the very least that will happen is that you'll look bad in the eyes of the judges. At worst you'll be at the mercy of a fighter who enjoys a significant advantage over you.
Escaping Ground Positions:
While on the defense in a ground position, you can use major transitions and minor transitions to drive your opponent back to less advantaged positions. Defensive transitions work exactly like offensive transitions.
Executing a major defensive transition from an Open Guard or a Half Guard position returns both fighters to Standing-Striking positions.
Transition Blocking:
You can block your opponents attempt at a transition using a transition block. Transition blocking augments your fighter's ground grapple defense skill and makes it less likely that your opponent's transition attempt will succeed.
Transition Reversal:
When you're on offense or defense, you can attempt to reverse your opponent's transition by as soon as he attempts the transition. If you're successful, you'll move from the disadvantaged position to an advantaged one, or you'll advance your position even further.
Submission Counter:
When you are on defense in Open Guard or Half Guard, you can counter your opponent's strikes with a submission as he throws a strike. If you do this while you're on defense in the Mount position, you transition to Mount-Down.
Stalemate:
When neither fighter is willing or able to attempt to advance his position, the referee breaks the stalemate by standing the fighters up. If you're in a disadvantaged position, you can use this to your advantage.