I’m sorry if the OP came away with hurt feelings, but the fact of the matter is that negligence–by both previous owners of these cars and by the OP herself–is the cause of the problems that she experienced.
As was already said, engines that are equipped with timing belts need to have these belts changed as a regular part of their maintenance. On most modern cars with timing belts, this is done at 105,000 miles or 8 years, whichever comes first. So, with cars that have over 150k miles on the odometer, anyone purchasing that car is taking a major chance by continuing to drive the car without investing the money to have the belt replaced.
There is certainly nothing wrong with being naive about car maintenance. However, all car owners need to be aware of what maintenance is necessary in order to keep the car running without incident, and someone who is not car-savvy has an even bigger need to become aware of necessary maintenance. This does not involve taking graduate-level courses and does not require engineering expertise. All it requires is the ability to open the glove compartment, taking out the mfr’s maintenance schedule (contained in either the Owner’s Manual or in a separate booklet with an appropriate title), and reading that maintenance schedule.
If no maintenance records exist, then the car owner has to assume that no maintenance has been done. That means that the responsible car owner will compare the car’s current odometer mileage to the most recent “big” maintenance list, and have everything on that list performed right after buying the car. For instance, if the car has 140k miles on the odometer, the 120k maintenance should be performed. However, it is also vital to backtrack a bit in order to see what other major maintenance jobs should have been done previous to that 120k maintenance. In this case, the OP would have seen timing belt replacement listed for anywhere from 90k miles to 105k miles.
Anyone can make a mistake when they purchase a car for the first time or whenever they venture into a new endeavor. However, it is important to learn from mistakes that are made the first time around. It just seems to me that after one disasterous timing belt experience, the OP would have taken some extra steps to avoid that type of situation with the next car. Her failure to learn from the first bad experience has been very costly, unfortunately.
Even though it is rather late in the game to begin learning about this topic, the OP can practice financial self-defense with her future cars (and with her wallet) by making sure that she has any potential car purchases vetted by a competent mechanic prior to purchase, and then by having the car maintained very well subsequent to purchase.
I would say something about one of the definitions of insanity being, “continuing to do the same thing, but expecting a different outcome”, but then the OP would accuse me of implying that she has emotional problems. I am certainly not implying any mental disability on her part, but if she continues to do the same thing (failing to educate herself about car maintenance and failing to replace vital components when due or overdue), then she might want to consider the implications and the consequences of that behavior.