Are you in Maricopa County?
You can enter the owner's name here: http://recorder.maricopa.gov/recdocdata/
Pinal County? go here: http://pinalcounty.org/Recorder/Search/
Search the documents to see if the bank has filed anything yet.
I know in pinal county the doc is SALE.
Brad and Relocation Guide have provided the best answers regarding finding out about the foreclosure.
Best of Luck,
You can search RealtyTrac.com or you can check out the Maricopa County website http://recorder.maricopa.gov/recdocdata
for recorded documents. Search your landlords name and you should get the recorded "Notice of Trustee's Sale" that will have the sale date on it.
If the home was truly foreclosed on and there was a noted attached to the front window or door, a realtor will soon be contacting you for eviction. It sounds scary and bad but it's just a process in order to get the property vacated. They will most likely offer you "cash for keys" which is a monetary stipend to help get you on your way and leave the home in the "broom clean" shape with appliances and structure intact. If it was foreclosed, you will most likely not be permitted to continue a lease so do start planning accordingly.