Sorry to hear, but not too surprising from what I've heard about Arizona's property values.
Buying a home for $120k, refinancing and having it appraise for $105k isn't an issue unless you need a higher appraised value to refinance, which I suspect you do. But you are going to have to provide more details about your situation, hit "Answer this question" to add more information.
Do you live in the property? How much is owed on your mortgage? Does Fannie Mae or Freddie Mac own your mortgage? If so, they have a program for people who are underwater, but others can use it, and it's where you can refinance up to 125% of your home's value value so you can take advantage of today's better interest rates. The websites to check if Fannie or Freddie own your mortgage are http://www.fanniemae.com/loanlookup & http://www.freddiemac.com/mymortgage - your lender probably is aware of that program though, ask them, or if you are already doing that refinance program... what value do you need in order to refinance?
Regarding the value, are there any better comps out there that the appraiser didn't use? Did you and your loan officer go through the comps that were most likely to be picked, and determine that $120k would be a reasonable value? Or were you thinking the value would come in at something else? Did you not even review comps before? Is this appraisal not even part of a refinance and you just got one ahead of time to see what you could be dealing with?
Have you discussed your situation with a local lender? Any reputable lender will be able to help you. If for some reason you can not do conventional lending you can try to use a hard money lender. Since it is an REO owner financing will not work.
Have you asked yourself why this property is priced at 33% of area comps and it is still available? Or why did they listed it that low? Make sure you are well informed before moving forward. When things seem too good to be true they usually aren't!
ABR - Accredited Buyer Representative