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In ArcMap XY data can be exported to a shapefile, or as a feature class in a geodatabase. If the coordinate values for some of XY data records are blank, that is the X or Y values are null, and you export to a shapefile, the exported shapefile will contain points with coordinate values of zero.
This is a known issue.
Exclude XY data records with null coordinate values when exporting to a shapefile. You can export null records to a personal geodatabase.