If you are asking can both of you be on title to the home and only her on the mortgage, the answer is YES.
However with a 650 credit score you are not precluded from getting a mortgage. The rate may not be as good as the girlfriends but depending on the program it may not be much different either.
Let me know if I can be of more assistance. I have spoken to clients on purchase deals like this where at settlement, the other party is left off title and it has caused terrible consequences as unforeseen events have occurred later.
Make sure that if your are both not on the deed, you DO NOT SIGN.
I'd be happy to assist you if you like.
Cornerstone Lending Inc
Southampton Pa 18966
215 953 0800
cell 267 992 7276
VOTED BEST IN BUCKS 2010 & 2012
NMLS ID 143960