The vapors from the chemicals given off by foam deterioration will permeate any cloth you cover the foam with.
I personally store in silicone impregnated gun socks inside zippered gun rugs. Ditch the foam as a storage solution.
You'll be happy you did it now, and didn't wait until the damage starts.
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 Igitur si vis pacem, para bellum -
- Therefore if you want peace, prepare for war.
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