Legal Question in Wills and Trusts in California

Sometimes, yes. You can't render yourself insolvent by putting your assets in any kind of trust, any more than you can do so by giving them away. That is called a fraudulent transfer.

It depends greatly on the precise terms of the trust and on the issue of whether a fraudlent transfer ( to avoid creditors) is involved. You would need counsel with expertise to look at what you are doing and advise you. If you already have the liability, it is doubtful it will accomplish your goals under any circumstances.