If they are in a participating community, then all buildings are in a "flood zone" and insurance is available. Whether the bank has to require flood insurance based on the specific flood hazard for the building has nothing to do with the grandfather rules. If the borrower had a policy in effect in Zone B and the building was in compliance when originally constructed, they could keep the Zone B rating. They could even purchase a new policy at a Zone B rating.
Some people, even if their property is not in a 100 flood plain, purchase flood insurance because they understand the risks (I for one). Since the original post asked "can the policy stay at zone B?", I assume they already have a policy.
"the insured would have the option of using the current rating criteria for that property or having the premium rate determined by using the BFE and/or flood zone on the FIRM (old map) in effect when the building was originally constructed (for those built in compliance)"
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