What function does a breather pipe have on a Chevy Corsica?

Not sure what you mean by a "breather pipe".

In the old days--before emissions, engines had breather pipes which vented blow-by and crankcase vapors directly to the atmosphere. Car co's wised up in the late 1960' s or thereabouts, both about the environment and increasing engine life, and installed Positive Crankcase Ventilation (PCV) systems.

Basically, blow-by (hot gasses, unburnt fuel, and condensation from the top side of the pistons that literally blows by the piston and rings, even in new vehicles) is very corrosive and damaging to metal parts in the bottom half of the engine. It also contributes to pollution.

PCV systems are set up to draw air from the vehicle's air cleaner down a tube, typically into one valve cover, through the engine head's oil return passages, through the crankcase, and into another tube on the other (we're talking about a V-6 or V-8 here, but they all work similarly) valve cover. This "exit tube" is controlled by a PCV valve which has a weak spring to prevent air flow going the wrong way, and to keep the PCV system from adversely affecting the engine's performance under certain load conditions.

The exit tube is ultimately connected to the carburetor or air horn of a fuel injection system, so there is vacuum on the exit tube. Thus while the PCV valve is open, the system "flushes" blow-by gasses and other crankcase vapors through the exit tube, and into the air-air/fuel mix path, where it enters the cylinders and is burned.

The V-6 3.1 Corsica's PCV valve is on the rear valve rocker cover, and the vacuum ("exit") tube is a model of crappy engineering, an S-shaped rubber hose that requires that the intake air plenum be removed from the top of the engine to replace.