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noun, な adjective
恥 is a "disgrace." If you 知らず then you don't know something. In this case, you don't know disgrace, and a person who doesn't know disgrace is a shameless person, because they don't care what disgraces them and what doesn't.
The reading is 恥 and 知る put together.
My brother is such a shameless liar. He told me he had no idea what happened, but he was the one who ate all my bacon.