With all due respect,
@TexasPhysician is partially incorrect. An outside party cannot sue a trust that was created in good faith. Unlike an LLC, one does not have have "ownership" of a trust or its assets. You simply benefits from a trust. Conceptually, it's not wholly unlike your grandmother who sends you a check in the mail for your birthday. You might be able to count on her money, but no medmal attorney would claim that her assets are on the line.
This is actually a key point of interest in the Epstein civil suits. Also why Maxwell correctly said she had no idea who owned the property she was in.
This is mostly correct.
OTOH, say that a trust owns a piece of property that later is found to need toxic cleanup because it was an improperly ran mine. The trust could be liable for clean up costs, and this could come out of what the beneficiaries would otherwise have been disbursed. Now, if you can show that the trustee is legally liable, ie they mismanaged things leading to the expenses, then you could come after the trustee for the money. Like any lawsuit, the success of actually obtaining a judgment is not just whether or not a court issues one, but is also related to whether or not the person is even "good" for it ie has financial assets or wage you can garnish.
This was a real-life example my own estate planning attorney gave me just last month when I saw him.
If the trust owns a property, and someone twists their ankle in a pothole in the yard or gets attacked by your "guard" dog, then there may be some liability for the owner of the property. Good homeowner's insurance that also covers the pet is essential. In my example it's not clear to me how much the trustee vs the trust has liability. Lack of maintenance leading to pothole might be on the trustee if they are responsible for maintaining the trust property. As far as the dog, it might be against the trust itself for allowing the occupant with the dog.
A trust can still have liability is my point. Otoh, if a trust owns your property, it would not be able to be sued for your PERSONSAL liabilities or business debt - ie if you are personally sued, malpractice, credit card debt, etc.
Keep in mind that any debt you have BEFORE setting up a trust, like student loans, can create an issue for a transfer into a trust if the debt isn't paid before you die.
I would highly, highly recommend getting with a very good estate planning attorney regarding all of this. You need to be careful how a trust owns your residence so that you are still free to buy/sell/reside/make improvements, and some of this can impact long term care planning and qualifying for medicaid for long term care (so now this gets to long term care planning). Remember, anyone can get into an accident or have some sort of CVA and end up needing long term care. All of this can be a bit more complicated as you plan with a spouse or want to leave an inheritance. Plus tax issues.
In no way do I mean to discourage the use of a trust for asset protection (in this case we're really talking about an irrevocable trust, those are the ones that offer these protections) but they are irrevocable. The issues are complex. Get a good estate attorney that can handle complex elder law/long term care planning issues/inheritance, and an accountant.