I would say that the tree/bush as is, is on its last legs. However, there will probably be shoots come up from the roots and if for some reason they don't you can take cuttings and propagate your Rose of Sharon from either old or new wood.
Rose of Sharon is a deciduous plant so the lack of leaves is probably normal depending on where you live at this time of the year/ That rotten hole in the base is not normal and will only get bigger and go deeper thus affecting the root system. It will probably survive another year or two but in the meantime when it leafs out again in the spring take a bunch of cuttings and propagate them
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