alternative fix:
If number of captured stones is equal (for example 0), then who has more stones on the board wins. Pass allowed.
It would be very painful variant. If you are too safe, you would never lose because your stone is captured, but you would always lose because not enough area/territory. If you would try to maximize territory fast you likely would lose because 1 of your stones is captured (opponent would immediately start to be safe after that). It would be hard to find balance.