When I use a website as a source, at the time that I access it for information, I will also save a snapshot of it in the Wayback Machine. Ofc theres no guarantee that the Internet Archive will be able to survive, but the likelihood of that is probably far greater than some random website. So, if the link dies, one can still see it in the Wayback Machine. This also has the added benefit of locking in time what the source looked like when it was accessed (assuming one timestamps when they access the source when they cite it).