Forums go out in one of two ways. Either with a bang or a whimper.
Sometimes, active user counts and posts per day just gradually circle the drain until the board feels like a ghost town, and then when it finally goes, no-one notices. A few people think back to that board they used to post on that one time, but can't quite remember the address.
Then there are the ones that go with a bang. The owner runs out of money, or walks away, and decides not to pass on the torch. The database crashes and the techies discover the backups don't work. Someone forgets to renew the domain name. One day you just try and go to your favourite board.. and it's gone. There's nothing. You can't figure out how to contact the owners or anyone who was on the board because that's the only way you talk to them...