If your cheap car blows an engine or transmission - just replace the engine or transmission. If it is an Asian model, you might be able to buy a low mileage used engine all the way from Japan for cheap. That is what we did with our aged CRV commuter. The car itself is good, has needed a few repairs but no car payment and didn't need to dip into savings to buy a different car.
Right now RockAuto is selling parts for cars this age for dirt cheap. $12 for a front strut? eBay had the AWD front to back driveshaft for $150 delivered. That is less than half what the local auto parts store wants. I'm doing a few repairs that I don't strictly need to - yet. Rear shocks are fine but 22yrs/303K miles old so I'm doing them anyhow since the parts were so cheap. New headlights b/c they were $35 a pair. Swaybar bushings are knocking. ~30 minutes in the driveway and $12.
As ChpBstrd posted, think like a Cuban. At least until the prices begin to stabilize again. I mean if we are discussing frugality in this forum, and this is important to a person, then this can save a person willing to DIY some money. Get a "YouTube degree" specializing in your brand machine. ;)
We have three 20+ year old daily drivers at our house. They do fine. I do recognize some folks may be up north dealing with bad roads and harsh winters so YMMV - literally.