Nothing.... until the next time you need to start it. Starters only fail while they're being used, and they're not being used while going down the road... so a starter really can't fail while you are driving the vehicle.
There is nothing that can go bad when a car starter goes out while you are driving. However, if there is a serious electrical shortage, then it can stop and die on the road. The car starter relay transfer electric current to the starter motor to start the engine. The car will be in trouble once it stops and must restart again.