There are many possibilities.
Obvious possibility number one: They're planning to do something criminal. Like maybe sign contracts, collect the money, and then never deliver. When the police come after them, they'll go to your address rather than the scammer's home. Then you'll be stuck explaining that you know nothing about any of this.
Two: All the bills get sent to you. I presume you don't just pay them, but then you get tied up explaining that you know nothing about these bills, possibly ending up fighting law suits or criminal charges. Hopefully you'd win in the end, but you could have a lot of legal bills along the way. And from the scammers point of view, the goal is to just keep things confused and attention off of them long enough for them to run off with the money.
Three: They've listed your house as collateral for big loans. They run off with the money, and when they don't repay the bank comes after you. After that similar to point 2. Worst case for point two or three is that the scammers forged your signature and a court doesn't believe you had nothing to do with any of it, and you end up stuck with the bills.
Probably other things I'm not thinking of off the top of my head because I just don't have the right thinking processes to be a successful scammer.
I would definitely contact whatever agency is responsible for registering LLCs in your area and tell them you have nothing to do with this company and this is some sort of fraud.