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I've never heard of that before. Are you the original owner? If not, maybe someone has used some type of cleaning product on it that's built up. Sounds kind of weird.
There is a rubber type coating over the plastic piece that goes around the stereo, AC unit etc. You will need to get a can of spray solvent ( engine grease remover) and spray it on the platic or a rag and you will be able to remove all the loose coating. Be careful not to get the solvent on any other parts.Once you start, it will take a little time but you can get it all off. It will clean up nicely and look like new. It may be easier to remove the entire plastic piece.