"What happens though if namecheap goes out of business during that?"

.COM agreement between registrars and ICANN requires registrars to regularily store all registrant contact infos in IronMountain and set ICANN as escrow, therefore allowing ICANN to contact all registrants should a registrar fold and allow them to transfer to another registrar. Another reason to keep the domain ownership informations up-to-date. [1]

[1]: https://www.icann.org/en/system/files/files/rde-agreement-09...

Namecheap can hand over their records to another registar before they go out of business or ICANN can step in after the fact and give their domains to another registar to manage. The new registar would likely reach out to introduce themselves.

Additionally there is a good chance that a different registrar would buy it up to acquire the customers and then transfer them to their system, etc.

This happened several years ago with a registrar I had at my domains at called RegisterFly. Upper management fraud and fighting led to the company spiraling, ICANN accreditation getting canceled and the site shutting down. ICANN transferred all ownership over to GoDaddy at the time.

https://en.wikipedia.org/wiki/RegisterFly

You can transfer it elsewhere at any point and you'll still get credit for the years you've paid for (though the receiving registrar will likely make you buy at least one additional year).