More details needed but generally yes, unless your ex becomes a citizen (or permanently leaves the US or dies) first. (And assumes the ex has worked those 10 years and been accumulating SS credit).
If you are talking about an I-864 you signed when he/she obtained permanent residency, yes, the obligations continue forever (not 10 years) until one of the conditions has been met: he/she becomes a citizen, has earned 40 quarters of Social Security credits, abandons permanent residency and leaves the US, or dies.
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