It is great that you are trying to do what you can to help your parents... ! Given the situation you describe, bankruptcy would not seem to be a strategy that would make sense currently for many reasons.
If the issue that is causing you and they to consider bankruptcy is the situation with the house, there are probably better alternatives. If there are other things going on, you have not said anything about what those are, so it is difficult to respond to whatever issues there may be.
If your parents dispose of any assets for less than market value, to any person or entity. those dispositions are subject to unwinding by the bankrutpcy trustee. Furthermore, if it was done in contemplation of bankrutcy, that can be deemed fraudulent, with a substantial risk of serious penalties.
The assets that are at potential risk in bankruptcy are those that have equity - meaning that the value of the items exceeds the bona fide secured debt. It is to that equity that the assets are to be applied. In Florida, the one generous exemption is in equity in homestead real estate, which can in some cases be in an unlimited amount. However, from your description, your parents homestead real estate has no equity. Other exemptions are quite limited, so if there is equity in vehicles, other real estate, bank accounts, stock, bonds, jewelry, household contents, etc. etc.
If I knew all the details, I may well have specific suggestions. It is impossible to learn enough on an internet web site to be able to do that, and besides, your parents' situation should not be discussed in detail on the open internet. I have an office in Boca Raton, and frequently assist people with mortgage problems. There are details and contact information on my web site, www.golantlaw.com - or feel free to email me at firstname.lastname@example.org
I think Ms. Golant gave an excellent answer. I just wanted to add that any transfer of assets regardless of who to can look bad. I think it's very important that you consult with an attorney about this that is knowledgeable about bankruptcy and alternatives to bankruptcy.
The previous answers are correct - bankruptcy may NOT be the solution to this problem, especially if the only debt that's causing trouble is from the two real estate loans. A better option may be to have an experienced attorney look at the real estate loans and figure out how to avoid foreclosure on those.
If you'd like to learn more about how and why to defend foreclosure instead of going into bankruptcy, check out our free 30-page ebook: