If an FHA appraisal comes in low, (say the purchase price was $320K and the appraisal comes in at $300K) the appraised value sticks with that property for six months in FHA's system. So, if the first deal falls through, for whatever reason, another buyer coming in WITH AN FHA LOAN has to get that appraisal transferred to their lender and must use that appraised value for their mortgage transaction. In the rare case the previous appraisal cannot be obtained, a new appraisal can be ordered.
However, if the FHA deal falls through and a new borrower comes in with a conventional loan, they can order a conventional appraisal and that FHA appraisal would be inconsequential. And given that FHA loans have gone back to "rare occurances" in recent years the odds of 2 FHA borrowers offering on the same property are probably pretty small.
But the takeaway would be if you have a FHA borrower out looking at houses, make sure you are checking if any FHA appraisals have been done on the property within the last 6 mos before you make an offer.