Most of these posts are way off...I work as a legal secretary for a lawyer who specializes in real estate law. I spend a lot of time working with this every day. That being said, I am NOT a lawyer, and am in no way qualified to give legal advice. (I am required to give that as a disclaimer.)
You need to google Arizona Landlord Tenant Act and read it through. It is a relatively new law in Arizona. It states that when a home forecloses, the new owner (whether it be an individual or a bank) MUST honor the lease agreement. This act was specifically put in place so that renters would not be kicked out if the owner was foreclosed upon. If your lease has expired, or you are on a month-to-month lease, you will have the same provisions as required in the lease agreement (read it, it is usually a 30 day notice). If you don't vacate after that, they are required to get a Forcible Detainer to get you to move out, which would involve going to court several weeks later, then being kicked out. Understand that if they get a Forcible Detainer, you may be liable for legal fees.
Some banks are willing to work with renters, and many more now than you would think. They may be willing to let you live there indefinitely so long as you pay the rent and are good renters. I have even known some banks to lower the rent to keep people in the house. If it were me, I would wait until the day after the trustee's sale and call the bank to find out who the new owners are and if they are going to let you stay. If you communicate with them, they will be more willing to work with you.
As far as whether or not to pay your rent now, some people would and some wouldn't when in your situation. If the current owner redeems (pays up) and the trustee's sale doesn't happen, or it is postponed (which happens all the time), the current owner could try to kick you out for not paying. Again, they would have to get a Forcible Detainer if you don't move out when asked. So there are a lot of "what if's" if you choose to skip your rent payment. Best of luck to you!