The homeowner has never been late or in default.
Sure, I do refinances all over the country on a regular basis for homes with present financing that is not Fannie/Freddie. Those loans are not eligible for HARP refinancing, which allows more wiggle room on property values, but in general, given adequate income/equity/credit, it's certainly possible to refinance a loan that was done outside Fannie/Freddie.
**The government doesn't do loans... ** Lenders do loans. If the loan is underwritten to Fannie Mae or Freddie Mac guidelines, the lender can potentially "sell" it to Fannie or Freddie anytime after closing.
I'm assuming by reading between the lines, you may be wondering about a HARP refinance. If you are underwater or your home has lost value, and have a Fannie Mae or Freddie Mac backed loan, there are good refinance options. FHA and VA also has cool streamline refinance options...