FHA Buyer wanting to do repairs during escrow

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I have a fixer property listed on the MLS with a flat fee listing. It's priced for buy and hold investors in the area. Not a lot of room for a rehab resale. Too many repairs for it to go FHA. Lots of interest and lots of showings after 5 days on the market. I agreed to respond to offers tomorrow.

The listing states cash only and "won't go FHA". But because there is so little inventory, half of the calls have been from agents with FHA buyers trying to scope out the repairs. Several have checked out the property themselves to assess the repairs. I have one agent who says her buyer can offer full price if I allow him to make repairs, at his expense, as they are called by the inspectors. Do sellers accept offers like this? It seems to me that the buyer's money is totally at risk. What if his loan doesn't go through? It needs flooring and paint and some major bath repairs.