Policy Premiums

What is the name of your state? Texas

Are policy premiums paid in advance or arrears? I received a notice from my insurance company that my policy coverage ended 10/31, however, my share of the premiums was deducted from my 10/31 paycheck.

That depends entirely upon your employer's accounting system. The law does not mandate that it be done either way. It is by no means unusual for health insurance premiums to be deducted from a final paycheck.

I get the distinct impression that you are trying to find something, anything, that you can sue your employer for. In addiiton, it sounds as if just so long as you get to sue them, you don't much care what it's for.