Many of the big or not so big corporations rely on brand monitoring companies to perform this kind of job (and often to manage their domain portfolio as well). Some Internet security outfits also specialize in domain/DNS intelligence, and provide services that overlap with brand management.
It's not possible to register every possibly infringing domain name (which would be a costly proposition) but besides doing the "obvious" like securing your brand name in the main extensions + some obvious typos, you can still, to some extent, monitor new domain registrations and detect names that look like typos of your brand, or otherwise look suspicious (for example your brand name followed by some keyword).
The main sources would be:
- zone files (for the TLDs/ccTLDs that make them available).
- certificate transparency logs
The bottom line is that new registrations are monitored to the extent of what is possible. Violations can and are enforced through different means, like private mediation, UDRP or court of law.
Trademark issues are not always clear-cut, black and white cases, so each domain has to be assessed on its own merits. In practice, it's very possible that brand owners will not do anything as long as the offending domain name is not being used for a nefarious purpose. Enforcement of TM rights has to be prioritized too, it's not always possible nor desirable to go after every offender.
The reason is that many offending/borderline domain names are registered by people with naive intentions (ignorance of TM law), or cybersquatters who expect some kind of compensation (finder's fee"), but whose actions do not pose an immediate danger to the brand owner. The domain name can still be put in a monitoring list once its existence is known, and the situation can change depending on how it is used.
Not to mention that web browsers have phishing protection mechanisms nowadays, that can help defeat attacks. Malicious domain names tend to be short-lived because they get reported, and suspended.