Back when I hosted my search engine on a PC out of my apartment, it survived several supposed HN death hugs.

Seems mostly to be a problem where your website is backed by a DBMS, especially when each page impression generates multiple queries. In that scenario, running out of connections probably isn't particularly difficult.

Only time I've actually been knocked offline was when Elon Musk tweeted a link to a blog post I made. That legit drove some real traffic. I'm not sure if it was the filedescriptor ulimit or the number of open connections that killed me, but I did actually blip for a few minutes.