Q. Who is liable for debts that we assign between us in our divorce settlement?
After property is divided incident to divorce or legal separation it is no longer community property; it is the separate property of the recipient. This separate property always remains liable to pay your own debts no matter when they were incurred. Even if that debt is assigned to the other spouse in the divorce division, you remain liable on the debt as between you and the creditor. Family Code section 916(a)(1).
Your separate property and what you receive at the time of the division is not liable for the other spouse's debts, whether incurred before or during marriage, and you are not liable for those debts unless the debt was assigned to you in the settlement.
If your property is nonetheless applied to satisfy your spouse's debts by a creditor, you have a further right of reimbursement against your former spouse, plus interest and possibly attorney fees.