Since 1998, only 0.05% of gun background checks have been denied due to the purchaser's drug use. Only 0.03% have been denied because the purchaser was under indictment.
But outlier cases like those are now part of the 2024 presidential discussion.
https://www.washingtonpost.com/politics/2023/09/26/gun-laws-become-2024-issue-an-unexpected-way/
Gun laws become a 2024 issue in an unexpected way

Donald Trump couldn’t buy a gun if he wanted to. Hunter Biden did, and faces criminal charges as a result.

The Washington Post

@pbump would the seller have filled out some sort of paperwork showing who he sold it to and the background check?

I wouldn't be surprised if he used a straw buyer.