Have a 2002 Chevy Prizm with about 50k miles. Engine bearing just blew on a used engine installed about 1-1/2 years ago. Cost 3500 to install a used engine with 44k miles on it. Used cars in this price range have at least 100k miles. Question is would you repair or replace?
It depends on the condition of the rest of the vehicle.
This will be the second time you’ve had to replace the engine in an 8 year old Corolla (Prizm). How have you been treating this car?
two “blown” engines on a newish car in 8 years, do you drag race? Or is it just the chevy on the downswing and why they went bankrupt syndrome? Or even more sinister, might it be your mechanic? do you ever change the oil, or say, add more when it is low? If I had a car this bad, I would have sent it to the junker for smashing a while ago. Whatever you do, dont put a thrid engine in this car.
The first time was due to neglect. My son did not change or check the oil, as he was told to do often. The second time was likely just bad luck, it was a used engine, don’t know the pedigree.
The rest of the car is in pretty good shape. Think we will put in another used engine - this time will be DIY 
You have to forget all the prior cost. That is money already spent and gone. The question you have is do you want to dispose of this car (what do you think it might be worth with a bum engine?) or fix it and what would it be worth then or fix it and try and sell it.
I suspect fix it and sell it is going to be be the best choice from a purely economic point of view.
A Prizm with only 50K miles is worth putting another engine in, IMHO. There are lots of Prizms out there with 250,000 or more miles on them.
Another option would be buy a rebuilt engine, which should come with some sort of guarantee.
Of course, someone has to check the oil periodically.