Shellac is one example of a resin that is solid at room temperature and becomes more plastic (softer) when heated or when under pressure. It is one type of lacquer, along with varnish, etc. The shellacs and lacquers used prior to the early 1920s were natural products made from bugs, tree sap, urushiol, etc.
One way to test for shellac or other older thermoplastic lacquers/resins is to provide a little bit of indirect heating (but never high temperatures or direct flame due to inflammability concerns) to a suspect area of the coin. If it softens up, then you can gently remove larger deposits using a rose-thorn or soft toothpick. Usually 120-150 degrees will do the trick. Watchmakers and watch repairers often use a fine tip low heat soldering iron or a "setting stick" (heated metal needle with a heat-resistant handle) for this purpose when setting jewels.
You can also use just acetone, of course, which is safer and will not damage the metal, and then work the affected areas in the same way. It will require more of a time investment to remove some of the tougher residue. This will not work on some types of varnish, acrylics, or modern synthetics, in which case you may try turpentine, methyl alcohol, and ammonia as alternative solvents, in that order.
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