Must a bank follow the conditions of a family's trust agreement before closing down a trust account and letting all the money be removed and the trust closed?
It's normally not up to the bank, but the Trustee. The Bank only needs to make sure that the Trustee is authorized to access and use the account.
If the Bank is the Trustee, then the account will be handled according to the wishes of the grantor of the trust.
There is no one answer. It will depend on the trust agreement and the particular circumstances.
Florida trust law may also apply.