Years ago, a company called "Lee Filters" sold air filters with a removable green foam cover over the main part of the filter. Would catch all the larger crud. I used to remove the green outer filter when dirty, wash it, spray filter oil on it, then put it back on the main part of the filter. Worked out great.
To this day, I cut a piece of foam filter material (thin enough that you can breath through) spray filter oil on it and place it over the stock filter. Saved me whenever I drive through a Dust Storm in AZ or NM. One time ion I-40 I drove through two in one day. Entire engine bay covered with red dust. Got to my place in Roswell and used a coin power washer to clean the red dust out. Pulled the air filter. Washed the foam filter. Stock filter was still clean. Still do this on one of my cars. Other car has a fiberglass filter over the regular filter, so I don't cover it with the foam filter.
BTW, the foam I use is the same thin foam that is sold in hardware stores for window air conditioning units.