Look up the Registered Domain name and see when it expires and buy that domain to take ownership of the domain name. Once you do that you can take ownership of the domain and shut it down as its now legally yours.
This is also a trick that some have done in the past to buy a domain name lease that the ownership lease on its name expired/lapsed and they pay to register that domain name and hold the domain name ransom to a company or individual to have to buy it back from whomever bought a domain name lease when a company or individual was sloppy and forgot to renew the domain name lease.
But in your case it would be to take ownership of that domain name as your own upon expiration and assuming it as your own on or after that expiration date. Places like godaddy support can help with letting you know when a domain name is set to expire even when its a domain that isn't your own initially.
However if this website is freely hosted and subdomained such as some free hosts main domain name with something like the following then its much harder to shut it down and would require contacting the web host of the free usually ad-supported hosting service requesting them to bring it down due to the fact that the owner is now deceased.
Example of subdomained would be like a website with a name of www . freewebhost . com / someones_webpage / index.html
(Without the spaces... spaces added to avoid making this an active link.)
