If you sue the LLC and obtain a judgement in your favor, the LLC would be responsible for paying the judgement. However, if the LLC has no assets, it may be difficult to collect the full amount owed. If the owner decides to close the LLC, this may make it even more difficult to collect.

One option to consider is negotiating with the owner to try to reach a settlement that is agreeable to both parties. This could involve accepting a lower amount than the full balance owed, but it would provide you with some compensation without the risk of pursuing legal action.

Another option is to consult with an attorney who can advise you on the best course of action based on the specific circumstances of your case. They can review the contracts and invoices, as well as the financial status of the LLC, to determine the best strategy for recovering the money owed to you.

It's important to keep in mind that suing an LLC can be a lengthy and costly process, and there is no guarantee that you will be able to collect the full amount owed. Weigh the potential costs and benefits carefully before deciding to pursue legal action.