Natural rubber residue would literally be a latex based substance. The product used for removing latex paint is called "Goof-Off". It smells like naphtha, so I tried lighter fluid on a spot of latex tear mender that had dripped onto a bed sheet and cured/dried in place. It removed most of the latex, the rest came right out in the next wash. It does not so much dissolve the latex as it does loosen it and make it fall apart. Naphtha is non-reactive with most finishes other than latex, so I suggest adding it to your list of possibilities. +1 for testing beforehand anything you try!
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"... Liberty is the seed and soil, the air and light, the dew and rain of progress, love and joy."-- Robert Greene Ingersoll 1894
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