My Macbook Air 2014 is stuck in an infinite boot loop because the SSD is not registering
If the SSD is not showing up in Disk Utility then it is likely that the SSD has failed or the hardware that supports the SSD has failed. The failure is likely coincidental to the OS reinstall and sale, but it can't be ruled out that the purchaser did something to the Mac. What that might be I couldn't tell you.
Realistically the only way to diagnose this is to open it up, preferably by a certified Mac tech, and see what is going on.
You are probably looking at having to replace the SSD (I think this Mac has a removable SSD) in your Mac.