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.
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.
