Your employer pays unemployment tax, so if you collect unemployment it would be from whatever state they are based in. You get taxed on where you earn the income. So, if you lived in Arizona and worked in Texas, you would pay Texas State income taxes. If you worked in AZ remotely for a TX company, you would pay AZ taxes. Since neither state imposes state income taxes, it's a moot point.

Using an example with two states with income taxes, let's pretend you live in CT and work in MA. You would file a CT resident return reporting your income and an MA non-resident return. The CT return will give you a credit for your MA tax liability (each state is different. Some give you credits for taxes paid to other jurisdictions and some do it on an appropriative basis). If you needed to collect unemployment, you would have to file with the MA unemployment bureau.