the car dies while driving for no reason. occationally starts then dies. wont start time and time again. then as if by magic it will just run like normal. battery is tight and good. fuel pump presurizes. if l remove the vacume line next to air intake that goes to a black cylinder about 4 inches long on the right side of the engine. it inturn goes down behind the motor, to where l dont know. the engine picks up about 2 houndred rpm and runs fine and l cant reprodue the problem(at least not in the drive way) what is that thing and is there another thing causing the main problem.

You may be referring to the emissions canister. The vacuum line is used to purge the gas fumes from it. Pulling the vacuum line off allows more air to the engine & would be like opening the throttle. This is why the engine speed increases.
The fuel pump is a common problem on the Cavalier. l know u said it pressurized but the issue is often that it fails while running at speed. At idle or even before starting, the pump will develop the proper pressure but at speed it is not able to pump enough fuel. It could also be related to a clogged fuel filter or inlet screen which causes the pump to run hot & seize. Once it cools a bit it runs again. To check it, try connecting a fuel pressure gauge & route the line out of the cowling area so that u can watch the fuel pressure when the problem occurs. Do not route the fuel pressure gauge inside the interior as this is not safe.