I didn’t quite understand your post. The company she works for pays her $1600/month rent? If she bought, would she herself be making the monthly payments or would the company do it?
Why does she want to buy if her rent is paid for? This makes absolutely no sense. She would be giving up a $1600/month benefit in exchange for an approximately $1800-2000 month liability. That’s a $3,400 swing. How could anyone think this is a good idea?
Personally, I think it’s outrageous that someone in your girlfriend’s position could get a loan for $250K. After taxes, the monthly payment would consume almost all of her monthly nut. Unfortunately, FHA will probably welcome your girlfriend with open arms only to see her foreclosed upon in less than a year.
Plus, it’s almost guaranteed that the place your girlfriend ends up buying will be worse than her current condo. I can think of no reason why she should buy.