Attacks vs Fortitude almost automatically hit.
Fortitude is a defense, it is nothing more than that. If your fortitude is 0, then attacks against your fortitude will hit (unless they are in turn an automiss (a 1 on the die roll)).
There are no game consequences to this beyond the fact that you become ridiculously easy to hit.
More importantly, this is almost entirely unlikely to happen. Even in the worst case, a PC's fortitude may be 8, and then it'd take 4 hits without a save before the PC was reduced to 0. This might happen but it would be incredibly rare.
Ultimately though, a defense reduced to 0 has no effect other than that the defense is 0. It could even be negative.