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I believe it’s for noise reduction. That’s also why they put snorkels on the air box. Open intakes can be almost as loud as the exhaust sometimes.
There is no foam on the inside of airbox. It is on the underside of tank & the outside of the air filter lid. I have cleaned out more than a few from sucking in the foam. If it is inside it got sucked in when dry rot happens. It crumbles & falls off. If you don't check your airbox at all, I would start.Aprillia uses a different item, use it to replace it under tank. The foam will cover your air filter BUT NOT GO THROUGH iT unless you have a crappy seal. You could use a GTM lid rim to hold filter so you can see in airbox anytime tank is lifted.I don't think you are burning foam unless you run no air filter.
Most of the foam is gone on them now, some went in where the snorkel was. If you have never looked in your airbox on a Breva, Norge, Sport chances are it's full of dry crumbly foam. Especially if you have run-ability issues. Aprillia uses a foil type of material. An engineers bright idea, for sure.