Under Account > Link Checker is a page that goes through all of the websites listed in your sources, and checks each to see if they still exist. Each will be listed out on the screen with a green (it is found) or pink (there was a problem) code indicating the status of that address. You can click the link to the website to test it yourself.
Also provided are a count of the number of records the source is attached to (only if there's a problem), a link to list those records, a link to edit the source, and if it is not attached to anyone, a link to delete. So you can update or delete it right there. An update does not appear immediately, but it is saved.
If an updated link can't be found, either (1) update the people attached to the link to reference a different source that is found, and then delete the source, or (2) move the out-of-date link to the "notes" field in the source, and label it as an obsolete website -- then you will still have it for reference, but no one will be trying to access it.
If the same address is quoted multiple times, it is only listed once here, but a number appears after the "edit" link showing how many times it is used.
Note that this doesn't guarantee that the website still contains relevant information, but just that it is still accessible. Cleaning up any bad addresses will help you to maintain your data and others as they browse your data. Please check your website sources when you can get to it, and check again at least every few months.