https://support.steampowered.com/kb_article.php?ref=3160-agcb-2555 Even if valve does go under, or run into too much trouble where it may just go under, it'll just get sold to someone else. The servers with the games, account credentials, logins, et cetera, would be under the control of another company, and the gamers will still have access to their games.
I wouldn't be surprised if any of the servers broke in the past, which is why any sensible business backs up the information beforehand.
