A registrar is the top level business next to the registry.
If you are talking about a smaller business they are probably a *reseller* for a registrar.
Most registrars if one of their resellers goes out of business they will push the accounts to another reseller. The worst thing that can happen to you is that your renewal prices go up, but then you can always transfer.
Just make sure your domain is truly registered to you, with your own email address and not the business you bought it from (if they are listed as a technical contact that is fine).
[icann.org...]
[rdearchive.com...]
ICANN's standard contracts require all registrars to escrow their customers' domain data, but ICANN is bad at enforcing its contracts. If you want to know your registrar's policies, ask the registrar.