If you are in need of refinancing and your credit score is under 500 then you have very limited options. The vast majority of home owners who end up refinancing with a credit score under 500 use hard money lenders. Hard money lenders are equity driven and pay no attention to a credit score under 500 when refinancing.In some isolated instances, you may qualify for FHA or Fannie Mae type financing if you have decent equity and a good 12 month mortgage history. Sometimes, Fannie Mae will approve a loan through there automated system even if there are some recent mortgage lates and a low credit score.
Another option is Freddie Mac. DU and AU systems are typically driven by payment history and liquid assets (typically 6+ months is good).
If your credit score is under 500 and you are wanting/needing to refinance you may want to consider working with a credit repair company to improve your credit scores so that you are able to refinance for a better rate. A credit repair company can sometimes improve your score enough to help you qualify for a refinance within as little as 30 days. The fee that you pay them to work on your credit and improve your scores will be well worth it if you can improve your credit enough to help you refinance and/or qualify for a much better rate.
If you are over 62 and have equity in your home you may qualify for a reverse mortgage. Reverse mortgages do not look at income or credit and can be a solution for borrowers with credit under 500.
Hard money lenders look at the value of the property and the loan amount. With loan to value ratios of 70% or less, hard money lenders can be a viable option to refinance as they do not look at credit for qualification.