Legal Question in Credit and Debt Law in California

Yup. The writing off of a debt is a purely tax related process (and a balance sheet adjustment for the creditor to make it more accurate). It does not affect the underlying debt at all. If you subsequently pay the debt, voluntarily or because it goes to collections and they force you to by judgment or otherwise, you will be entitled to deduct those payments from your taxes, and they will have to recognize the payments as income, rather than just reducing an account receivable.