Oil pump failure or Flush on 1996 Chevrolet Lumina

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My son's car stalled while driving to work. Is it possible that his dirty oil has clogged the system enough to cause zero oil pressure at the repair shop and can a system flush fix it instead of replacing the oil pump? Is it safe to run the engine during a flush? Trying to save the car but it's not worth another $750 repair.
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Engine oil circulating around the engine is like your own blood, the oil pump being comparable to the heart. Infrequent oil changes and or poor quality oil can cause sludge build up and oil passages to get restricted causing inadequate engine oil lubrication. Is the repair shop confident that replacing the oil pump will fix the problem or will after the oil pump is replaced will it then be discovered the rod bearings are bad or other parts of the engine are starving for oil.
My son is ready to junk it, but I'd like to see it running again so he can sell it for something. The repair shop is reputable but they report that there is zero oil pressure and that implies bad oil pump. I tend to think a good flush might be needed first to see if pressure returns. At 158K miles, undoubtedly the engine is worn. That's why I don't want to commit to $750 to r/r the pump, just to find out in the process that there is really $1000 more work on top of that to do. So, if running the engine to do a flush just ruins it more, might as well junk it and save all the hassle and time. I might be answering my own Q, but I'd like to hear someone else's opinion.