this is a really interesting thread topic, definitely something I've thought about occasionally. as far as accounts on other sites go, I would want them to stay up and dormant for people to view, and I like when forums have some way of noting when an account owner is deceased, it gives people an understanding of why they've disappeared from the conversation and gives them a chance to say their goodbyes.
if I were in charge of paying for hosting that'd definitely be something to figure out in the will or at least to plan for as a just in case. at the very least you'd want to give warning that your site will go down so that people who might want to archive it are able to, though ideally it'd be nice to have things live on for as long as they can. the internet is forever changing and things get lost every day, but there's something especially sad to me about sites dying with their webmasters.