No it doesn’t. The football coaches aren’t McDonalds workers that stop collecting money the second they’re fired. They have contracts and would be paid out for the whole season, assuming they weren’t let go for misconduct.
You can only fire 1 or 2 coaches at max during the season. Typically their responsibilities would be passed on to another current worker, like any other job. Then, nobody is going to be hired or would take an OC job for 3 games. That money is already a sunk cost anyway.
If you get let go a few months early, when you would have been replaced anyway, that is actually BETTER for you and your family. You can start planning your next move earlier, while getting paid.