I have very limited experience with this kind of stuff.
Archive.org keeps snapshots of certain websites stored. If you go to the website and enter, say ssnakess.com into the search, it will show you that this forum was archived on November 2, 2019, by Alexa Crawl. (Herpcenter is also being archived by Alexa Crawl.) The link to this site in its archive format is:
sSnakeSs.com
Looking on Archive's site, it looks like you can create an account and pay to have a specific website archived on a regular basis. It looks like Amazon, through Alexa Crawl, is already paying to archive herpcenter. If you go to Alexa Crawl's site, it looks like you can create a free account and use that account to, I assume, fill out a form to contact a customer service rep at Alexa Crawl. My guess is that you could tell them what is going on and see if they'll step up their archiving efforts.
Barring that, the owner of any website can transfer their domain and server contract to a new owner. The estate of the former owner of herpcenter could transfer ownership to a moderator or group of moderators as long as the new owner is willing to pay some fees and take over financial responsibility for the site.