The biggest mystery in the Social Security world is what is happening with the rate at which claims for Social Security disability benefits are being filed. There was a big run-up between about 2008 and 2010 followed by a prolonged decline. Various theories have been propounded but no one has a good handle on this. No, declines in unemployment cannot be the only explanation. If that were the case, the decline would have ended some time ago.
Jeffrey Schuh and Richard Leavitt gave a presentation to the Technical Panel on Assumptions and Methods of the Social Security Advisory Board on Disability Insurance: The Private Sector. It included the table shown below. LTD means Long Term Disability, that is private insurance, mostly an employee benefit. It's not stated in the presentation but I think EP stands for Elimination Period, that is the length of time after disability begins before LTD payments begin. EP-90 is a 90 day elimination period and EP-180 is a 180 day elimination period.
Note that this table would not include anyone laid off since they would not be eligible for LTD as an employee benefit. These would mostly be white collar jobs since blue collar employees aren't often covered by LTD, unless they're union workers and maybe not then.
This table shows a very significant decline in disability claims in a group that was little affected by unemployment rates and which was unaffected by circumstances at Social Security, at least in the rate at which they filed LTD claims. This is a table of the incidence rate per one thousand so birth rates in the 1960s are irrelevant. In general, this table just adds to the mystery.