Registrars are businesses and businesses fail. The good news is that the registration itself is the part that is protected; the risk is everything else that was bundled with it.
The registration survives
Registries require registrars to be accredited, and there is an established process for moving the domains of a failed registrar to another accredited one.
Your domain does not vanish. Its expiry date does not change. You end up as a customer of a registrar you did not choose, with a login you have to establish.
This is a genuine protection and it is worth knowing, because the instinctive fear, losing the name, is the thing least likely to happen.
What actually goes wrong
DNS hosted at the registrar. Many registrars provide DNS as a convenience. If those nameservers stop answering, the domain still exists and resolves to nothing. The website is unreachable and mail cannot even be addressed.
That is a total outage caused by a failure that did not touch your registration at all. There is more on why this failure is worse than a server outage in secondary DNS and what happens when DNS fails.
Email forwarding. Registrar-provided forwarding stops, and mail to those addresses is refused with nothing indicating why.
Auto-renewal. Settings and payment details do not necessarily carry across. A domain can proceed to expiry during the transition while everybody assumes it is handled.
That last one is the most likely way a domain is genuinely lost in this scenario: not by the registrar failing, but by nobody noticing that the renewal arrangement stopped existing.
The protection is separation
Keep DNS somewhere other than the registrar. That single decision means a registrar problem cannot take your site and mail down. The domain still points where it pointed.
It also makes moving registrars straightforward at any time, for any reason, since the DNS does not move with it. For doing it, see moving DNS to a third-party provider.
And know where DNS is, in writing. A surprising number of organisations cannot answer that question. Managing a portfolio of domains deals with the record that answers it.
The warning signs
Support that stops responding. A control panel that is intermittently unavailable. Renewal notices that stop arriving. Reports from other customers.
None of these is proof, and all of them are reasons to move rather than to wait and see. Transferring a domain is inexpensive and takes days; doing it calmly beforehand is entirely different from doing it during a failure.
What to do during a transition
Do not attempt a transfer while a domain is being moved between registrars by the registry: it will be refused, and a transfer initiated into an unstable situation is a way to create a problem.
Wait for the move to complete, establish access at the new registrar, then verify everything:
whois example.com | grep -iE 'registrar|expir|status|name server' dig example.com NS +short
Check the expiry date, the nameservers, the contact address and the auto-renewal setting. Then re-enable the transfer lock, which is frequently off after such a move. Domain locking sets out why it matters.
Only then consider transferring to a registrar you actually chose. There is more on the reasons it might be refused during this period in what to do when a transfer fails.
The same reasoning applies elsewhere
A registrar is one supplier. The same question is worth asking of the DNS provider, the mail provider and the host: if this company stopped existing tomorrow, what would break, and how would I recover?
For the host the answer is backups you hold yourself. For DNS it is knowing your records well enough to recreate them. For the registrar it is the separation above.
None of it is expensive. All of it is much cheaper before it is needed than after. There is more on the related question of what any supplier can reach in what your hosting provider can and cannot see.
Know where the registration actually sits
The company you pay is not necessarily the company holding the registration, and the difference decides what happens if one of them stops trading.
whois example.com | grep -iE 'registrar:|registrar iana|reseller'
The registrar named in the record is the accredited party. A company selling domains through them is a reseller, and a reseller failing leaves the registration intact with the registrar while you may have no way to manage it.
Read the field once for each domain that matters. A domain bought years ago through a small provider is frequently registered through a party you have never heard of, and that party is the one that would inherit the relationship.
Keep the ability to leave in your own hands
Recovery in this situation depends entirely on whether you can prove ownership and initiate a transfer without the failing company's cooperation.
Three things make that possible. Contact details on the registration that are yours and current. Access to the address those details name. And a record of the registration that you hold rather than one you view in their panel.
whois example.com | grep -iE 'registrant|admin email|created|expir'
Save that output somewhere outside the account. It is the evidence that establishes what the record said while the company was still operating, which is the question that gets asked afterwards.
Watch for the signs before it happens
Companies rarely fail without warning, and the warnings are visible to customers.
Support that stops answering, invoices from a name you do not recognise, a control panel that has not changed in years, or renewal notices that arrive late or not at all. Any of those is a reason to move rather than to wait and see.
Moving a domain while everything works is an ordinary transfer taking a few days. Moving one after the provider has gone is a process with no counterparty, and it is measured in weeks if it succeeds at all. Transferring your domain covers the ordinary version.