I'm not an expert, but that's not quite how LLCs work. LLCs limit the liability of the owner. Not the LLC.
Lets say I install plumbing in your house and it fails and damages your property, so you sue my company. If I'm a sole proprietor or a couple of guys doing business as a partnership then suing the company effectively means suing me (us) personally. If I lose and owe you $1 million, you can have my plumbing stuff seized to pay the debt, but if that doesn't cover all of it then I personally owe you the remainder. You can put a lein on my house and screw up my credit and put a collection agency after me until I pay off the debt.
On the other hand, if I have an LLC or a corporation, then the liability is limited to the property of the LLC or corporation. You can have my vans and warehouse seized, but you can't take my personal property like my house. If the LLC can't pay the full debt then it can owe you and make payments or something, but you can't "ruin" the owners.
In this case, simply "dissolving" the LLC wouldn't solve the problem. While it existed the LLC presumably had property, and that's what they would go after. If you tried to pull a "The LLC didn't have any property" then they'd probably toss you to the IRS for running an illegitimate LLC. And when the IRS was done auditing you, the patent guys would come back and go after you personally.
I'm definitely not a lawyer or any kind of business expert, though. If anybody knows better I'd also be interested.
I'm not a lawyer, but I've got a LLC equivalent and you're almost spot on.
If I own 25 of a company's shares, and let's say the shares are worth $1000 each then it means they can only claim a maximum of $25000 from me. Which is actually my investment in the company. So the worst thing they can do is take over my shares. Along with that, they can hypothecate any and all equipment that has been purchased in the company's account. So, the company car, company computer, server space, domain name, tables, chairs, office space etc.
What they cannot do is physically come into my home and forcably take my wife's jewelry and my personal computer. They cannot take my television or my car. Because those have been bought on "my" money, i.e. the salary that I'm claiming from the company.
This is LLC/WLL.
But what I'm interested is a bit different. Say, I run a business called algorithms.com with my company registered in Sweden. If tomorrow a patent troll in Texas files a suit against me, it's obvious that the US DOJ cannot shut down my business. But can they seize the domain name, only simply because it's a .com instead of a .se or a .whatever else
Limited liability refers to the liability of the shareholders/investors for the obligations and judgements against the company. Their liability is "limited" to the amount of their investment.
Contrast with a partnership, in which the owners/investors are subject to potentially unlimited liability.
For example:
LLC A settles a lawsuit for $10 million. Investors B and C's liability is limited to the size of their investment (we'll say $100).
Partnership X settles a lawsuit for $10 million. Partners Y and Z are each liable for the $10 million (the opposing party only gets to collect $10 million once, he simply can choose to go after either or both partners for payment). The opposing party can go after Partners Y'z and Z's personal assets, unless they declare bankruptcy.