I'd carefully review the lease agreement and other agreements with the section 8 housing authority you have been working with. Chances are there is a term in the agreements that applies if the tenant dies during the lease term.
From an equitable standpoint, it does not sound particularly equitable for you to receive a cash windfall because a tenant dies shortly after signing a one year lease. However, review the terms of the lease and see what it says.
Your rights should be spelled out in the lease agreement and corresponding paperwork, and in the off chance they are not, I assure you that you are not the first landlord in Florida to have a section 8 tenant pass away during a tenancy. A skilled lawyer will review the case law in Florida for similar circumstances, and will advise you appropriately how to proceed.
I would recommend you gather the paperwork and consult with a landlord-tenant attorney in the Tampa Bay area.
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