They could assign it to you, but that would mean the Life of Loan coverage they probably have now covers you and their certificate would be useless to them. For HELOCS, and other long term loans, I always tell our banks to get an independent Flood determination. If we're doing a joint loan with our mortgage depart - i.e. construction/perm where we do the construction and they do the perm, the bank pulls the flood for the construction period and assigns it to the permanent lender at closing. So, we're all covered for one price to the consumer.
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My Opinion Only.