There are only a billion numbers. Counting everyone who has already died since they were introduced, and all the "taxpayer id" numbers that are issued for people who don't have real SSNs, how long until we run out? Or are they already being re-used?
They don't get reused.
There are about 70 years left.
The government is punting the problem to future people and there's no solution yet.
"Q20: Are Social Security numbers reused after a person dies?
A: No. We do not reassign a Social Security number (SSN) after the number holder's death."