1994 Buick Century Diagnosed with "broken cam shaft&qu

HI there: We have a 1994 Buick Century wagon 3.1 6 cylinder with about 134,000 miles on it. Recently it experienced an extreme loss of power. It was towed to a air conditioning specialist shop that had recently done air conditioning work for us, he's also a general mechanic, but I don't think he does much engine work. He has diagnosed it and tells me that there is no oil pressure and that the cam shaft is broken, yet the engine runs, though very roughly. Can an engine run with a broken cam shaft? And have you ever seen a Buick with a broken cam shaft? The mechanic thinks that the back side of the cam shaft delivers power to the oil pump and that the back side is not getting power from the front drive side, so no oil pressure, and the front side is powering a few cylinders, so that's the rough running. He's suggesting replacing the engine with a low mileage used engine, for about $1,800, and I"m leary that a broken cam shaft is an accurate diagnosis. Thanks for any help you provide to help me sort out a reasonable next step.
Eric