If a woman marry a man that owes child support, can she be held liable?

For pre-marital debt, the pay order is like this: his separate property, community property, and your separate property. Theoretically the child support incurred in marraige will be community debt that you would be liable to some extent. You income has no bearing on the support amount. It may, in a sense, lower the support a little since together you would pay more taxes.