The legal entity side where you the person who paid for the service is now deceased is a small part of the problem. Once the credit card company knows you're dead, so are your cards. Then you need to figure out how to get the service provider to change payment method without them realizing that the person who's name is on the account is deceased. If you care so much about this scenario, your best bet is to form some form of LLC that itself owns the domain, service contracts, etc. Make your executor/spouse/meaningful person a signing officer. This has the added benefit of skipping over probate issues as well.
The bigger issue is the content/tech side. All sites need maintenance. All service providers eventually go out of business or get acquired. Bit rot is a thing. Your best bet for future-proofing is to either publish static HTML, or have a backup that can be published as static html after the fact. Either way, you really need to have a designated geek to help finish your affairs.
And, after all that, you still need to figure out how to pay for the hosting perpetually. Maybe directing an annuity to be established is the right thing? No idea.
With all that said, sometimes its nice to leave a legacy. E.g. http://www.penmachine.com/