When someone assumes a debt it would be my opinion the lender is making/extending credit to the person assuming the debt therefore it would be a designated loan subject to the flood rules.
However, remember the recent conversation in the threads about re-using determinations.
As long as the the determination is for the same lender, on the SFHDF, is less than 7 years old and there have been no map changes then you can follow the following formula:
Same property + same lender = same determination
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The opinions expressed are mine and they are not to be taken as legal advice.