My E36 325i BMW has about 302,000 miles on it and runs like a champ. I bought it at 140k mileage. At first I changed the oil every 5-7k miles with Castrol 20w50. In the last five years while serving as my daily go to work driver (80 miles per day), it has gone several times to 15k miles before oil changes with no issues. Obviously 3000 mile oil synthetic oil changes are not required in modern cars to achieve long life as proven by my old trusty BMW. That said, I do try to follow the owners manual on my newer cars but I do not get too concerned if I go a couple thousand miles over from time to time.

Someone mentioned that this is the reason why they don't buy used cars, actually it's not a concern because it's so easy to check for this particular type of abuse/lack of maintenance. Any used car that I ever look at, one of the first things I do is open the oil cap and look at it and the inside of VC cover. On most engines, you can clearly see a rocker assembly or two plus part of the cam if the cap is directly on the VC. It gets harder to check if the engine has a long filler neck going to the VC but those are usually easily removable.

The great thing is that if an engine went for a long time between oil changes even once, the evidence is there. Black coloring and in extreme cases, sludge will be visible. In a properly maintained modern gasoline-powered engine, the valve train will be honey-colored or at worse brownish and absolutely clean of deposits. On diesels, black coloring is normal but there should be zero sludge. There are obviously several other tests and things to check, (blow-by, compression/leakage, etc.), and service records proving regular maintenance are always nice. But even w/o any records, a good eye can see a lot. Equally important on most engines is the condition of coolant passages and they are a lot harder to check than oil history. A history of clean, correct coolant is important on any engine but with aluminum it's life or death.

I'm not familiar with engine replacement cost on those vehicles, but yeah... if they are cheap enough then go that route. Clean up the gunk you can reach, change your fluids, and cross your fingers. At worst, it seizes and you perform an engine swap.

Or you sell it on Craigslist with the standard disclaimer, "It was running fine when I parked it."