In Florida, the buyer of a property typically receives the deed at the time of closing. The new owner then gives a mortgage to the lender - the mortgage is a pledge of the property as collateral for the loan or "note". So the owner almost always holds the deed, whether the mortgage note is paid off or not. A deed is an instrument of ownership. You don't need to have the actual piece of paper to "hold the deed" - most deeds are recorded at the courthouse so a copy is always available if ownership needs to be proven. When the mortgage note is paid in full, the owner of the property should receive proof of that from the lender, which should also be recorded at the courthouse. You can check much of this through public records at the county courthouse - often available via an online search.
Please don't take this as a legal opinion or legal advice. If you have legal questions - direct them to an attorney who practices real estate law.