Well... think of it this way... What does the PSU do? It converts AC input to multiple DC output.
So inside, you have parts on the AC side, and parts on the DC side.
If it fails on the AC side, it's very unlikely there's any damage beyond the PSU "blowing up". If the failure is on the secondary, it can cause damage for many reasons.
Protections have improved a lot over the years, but not all PSUs are created equal. I remember about 20 years ago or so, MSI boards were the worse. Their VRMs would heat up and sometimes even burst into flames. The CPU would fry AND THE PSU! The PSU would actually turn into a motherboard killer. If I had an MSI board that caught fire on the bench and then went on to test another motherboard with the same PSU, that PSU would then kill that motherboard. I would have to scrap the PSU and get a new one. Wish I knew then what I know now I would open the PSU up and figure out WHY the PSU all the sudden turned into a killer... but damn those MSI boards were horrible. Lost so many good Athlons back then.