Can an airline prevent a passenger from boarding the plane during a layover because they left and re-entered the transit area?

I'll summarize the answers that the question received in the comment section:

1. The airline simply tries to enforce the country's rule: they don't add extra rules.
2. If a passenger leaves the transit airport, then they may not be able to legally enter the destination country, esp. due to COVID-19 restrictions.
3. In theory, one is not allowed to exit the transit area, as the airline is not paying airport taxes there for processing passengers through those channels, though it unlikely to be enforced.

The answer is based on the following comments:

• I believe it would be the country's rule which the airline has to honour. Airlines tend to check your eligibility for flying before you board. Under normal circumstances, they check whether you have a visa for the destination country, or are simply allowed to enter. Now, with COVID, the destination country might have restrictions on passengers from the transit country, but not (or differently) on passengers from the originating country. So, a passenger leaving the transit airport might mean different restrictions come into effect and the passenger might not be able to travel onwards. – MastaBaba 7 hours ago

• There may be some confusion with the fact that unless you have a stopover rather than a layover, you usually won’t be able to get your checked bags (or check new bags). This is clearly under the airline’s control (directly or indirectly if they outsource part of the ground handling). There may also be the issue that the airline may not file API-type info for transit passengers. In theory you are not allowed to exit (as the airline is not paying airport taxes for your processing through those channels), but I doubt this can be enforced in most places. Details of country YYY would help. – jcaron 7 hours ago

This is simpler than it looks

Can the airline prevent the passenger from exiting/re-entering the airport YYY during their layover at airport YYY,

No. The airline has no legal authority to do so.

and/or prevent the passenger from boarding the flight because they exited/re-entered airport YYY?

Yes. If by leaving and re-entering you violate a rule or condition that is required for entry into country C.

It changes your status from "coming from A with transit in B" to "coming from B" which may trigger a completely different set of rules (Covid or otherwise).

The practical aspect of this depends on the details. In some cases, the airline may not even be able to detect that you left and re-entered. In other cases, you may already get snagged at security since some magic stamp is missing from your boarding pass.

The passenger is allowed by countries A, B, and C to exit/re-enter the airport YYY during their layover at airport YYY

Countries A and C have no authority whatsoever to dictate who country B allows in, allows transit, allows to land (but not disembark) or denies altogether. Border admissions to country B are the sovereign right of B and B alone.

(which implies that country C is ok with the passenger leaving the transit area in country B before entering country C).

Assuming you mean travel in Covid Times, then yes this part can be a factor. In early 2020 travelers were considered to have entered the country the moment the wheels hit the pavement. Obviously this created a huge problem and has since been sorted out. As long as you stay in the transit area you are typically not considered to have entered the transiting country. Once you cross immigration you have officially entered and the arrival rules for country B and A now apply when you arrive at C. There are some easings for places where, for example, you have to change terminals but not airports.

In the Before Times we had the Israel problem. Some countries (mostly theocratic Arab states) would not admit people if they had an Israel entry stamp in their passport. You don't get one of those if you stay in the transit area. You also didn't get one if you asked Israeli immigration to not stamp your passport, which they were happy to accommodate.

In broad terms, the airline cannot stop you walking out of the airport at an intermediate stop simply because they do not know it happened. That's between the traveler and immigration. Other comments about airport taxes may apply, but in general a transit passenger is not charged taxes and departing within 24 hours of arrival is usually considered "transit". Plenty of connecting flights leave the next morning.

Also in broad terms, airline staff tend to take a stricter view of immigration rules than immigration themselves. One reason is the fines the airlines get if they accept a passenger they should not have accepted. It's a lot more than the airfare. Another is immigration deals with only their own rules, while airline staff have to read up on the rules for every destination they service. And the check-in staff are sometimes contract employees with minimal training.