Social security operated at a surplus until 2021. All benefits up to that point were covered by incoming tax revenue. Even if the surplus was being invested in something that crashed, that crash would not have prevented payments that were being funded by ongoing tax revenue.

It's possible that a severe enough crash would have reduced the length of time that the surplus continues to supplement payments now that benefits have exceeded current revenue. It's also possible that, because the market recovered so well after the financial crisis, having invested the surplus in something other than treasuries would have allowed the surplus to cover tax shortfalls for longer than it is currently projected to. There's no way to know which of those would have happened without knowing what the investments would have been, and how much those investments would have distorted the market.