You learn something new every day in GIS.
If I open a shapefile attribute table, select an attribute, and use the field calculator to populate the field with an expression such as...
attributeX / 0
I get an error all calculated values were invalid, no rows were updated.
attributeX / attributeY returns no error even if values in attributeY have zero values, In fact, it populates those values with zero values.
This is disturbing.
If I do this same test in a geodatabase I get null values for the zero division rows.
I understand that there are data structure limitations. Shapefile fields are not nullable... but the shapefile example ought to give some warning!