If I buy a candy bar from a bankrupt chocolate company I don't inherit any liability from the candy bar.

"Breaking up" a company by selling its assets and distributing the profits to creditors absolutely does vanish the liability.

I didn't say it removed the liability of the company. It just means that the company that is left after selling off its profitable assets has the burden of the liability but with nothing but literal toxic assets. They can use the proceeds of the sales to start paying down the debts.

The assets sold would obviously not be the toxic assets.