Most likely the travel agency reimburses the carrier at the end of the month, etc. In other words, the carrier extends credit to the agency. If the agency is not solvent then the carrier stops accepting passengers booked through that agency.
That explains a lot. I didn’t see just how they could be stranded. Tours or packages I guess.
One company I worked for used Thomas Cook, both brit companies so there you have it. Their service was good but not essential to me. I used them because they were available and had a global 800 help line that could do a pretty good job of working out problems but especially changes I often had to make in my 5 years of globe hopping 250 day a year travel schedule.
The international travel service I most liked, only used once but depended on was International SOS for medical emergencies. I know people who needed it and it was good but a whole lot better than nothing. Arranging air evac to anywhere is not for the novice. I went to an SOS doc in W. Africa for a stomach bug. He was Lebanese / French and very good he also took care of the health checks and food safety for his BIL restaurant in Lagos, Nigeria. It took a real sense of adventure to eat Sushi in Lagos! That is not where I got sick though. Probably our favorite Thai restaurant.
In this case the travel agent IS the carrier - TC has [had] its own fleet of planes.