How to claim debt back from a Florida LLC once its administratively dissolved

This is a great illustration of why creditors normally make the individual incorporators sign on the dotted line, not just the LLC. You would have to try and "pierce the corporate veil" in order to hold the married owners liable instead of the defunct corporation. A collections attorney can explain what this involves and the various facts which courts will use to make this happen. Find one on AVVO.

I will answer this question for you, as best as I can.
A dissolved corporation or LLC in Florida continues its existence for the purposes of winding-down.
So you can sue the corporation (I recommend you do this ASAP), get a judgment, and then set up discovery in aid of execution or set down a Debtor's Exam under Fla. Stat. 56.29.
At that point, if the original managing member appears and testifies, you can find out about the assets. If the money or property has been transferred to the managing member or others, for less than fair consideration, or transferred to an insider, it may be set aside by the judge and ordered paid or sold and the money paid to you.
Alternatively, you can request that a receiver be appointed to take over liquidating the corporation. However, that costs money.
If someone owes money to the LLC, you can garnish it. If there are bank accounts, you can garnish those.

As in so many situations, it depends. Once an LLC is administratively dissolved, if the owners continue to operate under the name of the LLC it is possible for them to become personally liable for the debts of the LLC incurred after the dissolution. If the LLC was not properly operated it is possible, but not easy, to tag the owners with the entity's liabilities. This area is somewhat complex and would require the analysis of an experienced collection attorney.

The simple answer is that if the owners signed a personal obligation to you along with the company, forget the company and sue them directly. You're going to need a lawyer for this either way though.