Oh yeah, it could happen. Last year TWC-Austin dropped KXAN (NBC) for a few weeks. I don't know how it ever ended up getting worked out, but TWC put the station back on.
I'm not much of a Fox viewer (any TV, actually), but I do watch the local news on KXAN in the morning. I think they have better weather folks, but that's just my opinion.
If they actually drop Fox, I will probably drop TW like a hot potato. Last year it was the local ABC station that TW dropped for a while. That was the second time they had a disagreement and dropped the ABC station. Funny that Grande the other Cable available down here doesn't go through this nonsense.