There are different types of cells in the heart so it depends on which type of cell you are asking about. Some heart cells can be replaced because they are derivatives of bone marrow stem cells (shown in rats by using male bone marrow stem cells in a female mouse and detecting Y chromosomes in the heart much later). Some heart cells are smooth muscle and can likely be replaced by derivatives of smooth muscle stem cells. I do not believe this is a common occurrence (or at least not as common as we would like).
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This is highly uncommon.