Operate Steam in offline mode, in the short term. You would only have to worry about it when you need to get a new PC, change your hardrive etc.
Having said that, businesses with that many customers rarely just close the doors and everything ceases to exist. The platform itself is an asset, so someone would buy it (for a song) and allow it to continue operating. It would be an ideal crowdfunding opportunity.
It's the same with many other companies. What happens if Costa Coffee goes bust? How will I redeem my "Buy 5 coffees get the 6th free voucher"? I own that coffee! What about football / theatre / cinema / gig tickets bought in advance?