I'm sorry to hear of your situation. Unfortunately, you're not the only one to be facing this, as it is a huge problem right now in Arizona. In short, by the time the house is foreclosed, you will have to move out. Since you found the Notice of Trustee's Sale, what is the date set for the auction? It should be about 90 days away, which will hopefully give you time to find another home to rent. If you're still not sure how to respond, then contact your landlord immediately. Then you may want to contact an attorney. There's no easy,simple answer to your question, so do some research, too.
Best of luck to you!