This does not agree with what the Social Security Administration has published:

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. Even though we have issued over 453 million SSNs so far, and we assign about 5 and one-half million new numbers a year, the current numbering system will provide us with enough new numbers for several generations into the future with no changes in the numbering system.