I'm not exactly sure what you mean by being liable for his Social Security, but I'll explain a few relevant points.
If you are divorced after at least 10 years of marriage, you can collect retirement benefits on your former spouse's Social Security record if you are at least age 62 and if your former spouse is entitled to or receiving benefits. If you remarry, you generally cannot collect benefits on your former spouse's record unless your later marriage ends (whether by death, divorce, or annulment).
The receipt of benefits by an ex-spouse does not change the amount of the monthly benefit of the spouse upon whose earnings record the benefits are based.
Eligibility for the benefits is not dependent upon authorization by the ex-spouse; however, divorce agreements are far-reaching. You should discuss this with your divorce attorney if your spouse is attempting to include any restrictions on your eligibility.
