That registration has value - its an asset that makes recurring revenue - so they'd likely transfer (sell) it to another registrar. You'd get an email with a link to a new backend to login to etc. This has happened to me numerous times over the years (they usually call it an acquisition, but I suspect many of them were effectively going out of business). It is a slight pain to learn a new system, but you never lose the domain or anything.
Worst case scenario Verisign or ICANN would step in. The registrar doesn't own the domain, you do. They are just the custodian. Similar to how a stock broker doesn't own the stock you hold with them and even if they go out of business, you still own the stock.