Anamon: I tried figuring out once where that very persistent rumour came from. My best bet was that it was probably a statement made by Valve in the very early days of Steam, when they still only sold their own games. Even ignoring the fact that if the reason for a Steam closure was that Valve went out of business, there would be no Valve to develop and deliver the promised crack anymore, and the fact that many games rely on much more than just Steam, the idea is mind-bogglingly naïve. Do they think all publishers on Steam agreed to Valve being allowed to just remove the DRM? Or do they believe that Valve would make an effort to renegotiate deals with all the hundreds, maybe thousands of rights holders, just to give their ex-customers a freebie? :D
AFAIK, the "source" for this claim was an alleged forum post from a Valve representative (or Gabe himself?) made long, long ago, not long after Steam opened. (And obviously this post has long since vanished, if it even ever existed.) Since then it's been repeated over and over so much, that it's now accepted as canon that Steam "officially" stated that they will issue a patch to remove any dependencies on Steam's online DRM if Valve were to go out of business.
Nevermind of course that Valve has never released any official statement to this affect, and Steam's own SSA states that they're neither liable nor responsible for what happens if you can't use the Steam service.
The best I've been able to come up with is a
reddit thread from 2013 but even that proves nothing. Assuming that reply wasn't faked, it doesn't outline the details of what measures they have in place (Backup servers supported by an emergency fund managed by an independent group for a set amount of time? A miracle universal offline patch for all of their games?), nor does it outline the sustainability, terms, conditions and/or limitations of those measures going forward.
That leaves us where we started - a vague (and arguably dubious) promise from corporate, and irrational beliefs based on hearsay.
Anyway, short of something truly catastrophic, the most plausible scenario I can imagine is Valve being bought out by a big company with the resources to afford Valve's estimated market value of ~$3 billion (Microsoft? Vivendi?). After that, Steam itself would be gutted and/or EOL'd in favor of another platform branded under the Steam name, that would better suit the new owner's corporate agenda -- but again, this is just idle speculation on my part.