Air DOES get cleaner. Dirt makes the effective pore size of the filter smaller, so smaller and smaller particles get filtered out.
All pleated paper filters do this.
If you run the air filter 'until the engine quits', you have gone far beyond the useful life of the filter. Typical values for filter replacement vary from 20 to 30 inches of water. This corresponds to a pressure differential between the dirty and clean sides of the filter of .72 to 1.08 psi. No engine is going to quit running at those restrictions, but it is time to change the filter.
All pleated paper filters do this.
If you run the air filter 'until the engine quits', you have gone far beyond the useful life of the filter. Typical values for filter replacement vary from 20 to 30 inches of water. This corresponds to a pressure differential between the dirty and clean sides of the filter of .72 to 1.08 psi. No engine is going to quit running at those restrictions, but it is time to change the filter.