What happens when they run out of SS numbers?

[LSLGuy]

Here’s a (very) old thread on point:

How long until we run out of Social Security numbers?

Google has failed me, as has Cecil’s column archive. I know the Social Security Administration is re-using the numbers of some dead people now, but with longer lifespans I’m thinking that’s probably a stop-gap measure. Will the numbers eventually have to grow longer by a few digits? What’s the Straight Dope?

I recall us discussing this topic afresh sometime in the last couple of years. I’m not able to guess the right combo of words to find the title now, nor find my contributions to it.