Forced to Resign or Terminated?

My boss asks me to resign with one weeks pay for each year I worked OR find other employment within 30 days, if I don't find another job he will terminate me on the 30th day. I am uncertain of this, not to mention if I'd be able to collect unemployment till I do find another job. Nothing was put in writing and I was asked to keep it confidential. Confused and afraid of what lies ahead!