I don't think they put their assets in her name, because she's in bankruptcy too. That would not do anything helpful for them.
No bank would lend them money for at least ten years. But their families are rich, and Joe's dad already bought a pizzeria for them.
The 10K/month is a gift. You don't pay income taxes on gifts. But the "giver" pays a gift tax on it. Once you have given more than $13,000 in cash to one person annually, you have to pay gift taxes further cash gifts to him/her. If the money is paid directly to a bank or other institution (to make a mortgage payment or whatever) there is no gift tax incurred.
The contractors cannot file liens unless the Giudices' Chapter 7 bankruptcy relief petition is kicked out of court. If it goes through, their debts are discharged including the money they owe to the contractors.