Can an employer wrongfully terminate you and then stop unemployment benefits?

If you didn't have a written contract of employment that said otherwise, you were an employee "at will," which means that the law doesn't expect the company to have any  reason at all for letting you go.  So firing you for refusing to go to the office when asked, even if you had an excellent reason (not committing DUI), isn't something that's going to get you anywhere in court.

The company might try to stop your unemployment benefits, saying that you were fired for cause.  If so, you'll get a notice, and you need to read that notice and do what it says to appeal the denial, so you can get a hearing and tell your side of the story;  employees do win quite a few of those hearings.