Despite extensive genetic analysis, the evolutionary relationship between polar bears (Ursus maritimus) and brown bears (U. arctos) remains unclear. The two most recent comprehensive reports indicate a recent divergence with little subsequent admixture or a much more ancient divergence followed by extensive admixture. At the center of this controversy are the Alaskan ABC Islands brown bears that show evidence of shared ancestry with polar bears. We present an analysis of genome-wide sequence data for seven polar bears, one ABC Islands brown bear, one mainland Alaskan brown bear, and a black bear (U. americanus), plus recently published datasets from other bears. Surprisingly, we find clear evidence for gene flow from polar bears into ABC Islands brown bears but no evidence of gene flow from brown bears into polar bears. Importantly, while polar bears contributed <1% of the autosomal genome of the ABC Islands brown bear, they contributed 6.5% of the X chromosome. The magnitude of sex-biased polar bear ancestry and the clear direction of gene flow suggest a model wherein the enigmatic ABC Island brown bears are the descendants of a polar bear population that was gradually converted into brown bears via male-dominated brown bear admixture. We present a model that reconciles heretofore conflicting genetic observations. We posit that the enigmatic ABC Islands brown bears derive from a population of polar bears likely stranded by the receding ice at the end of the last glacial period. Since then, male brown bear migration onto the island has gradually converted these bears into an admixed population whose phenotype and genotype are principally brown bear, except at mtDNA and X-linked loci. This process of genome erosion and conversion may be a common outcome when climate change or other forces cause a population to become isolated and then overrun by species with which it can hybridize.