The vertex numbers are shifted up one (with the last vertex changing to #0) and the m-value of the last vertex is incorrect in the output of the Intersect tool if the start and end vertices are coincident.
Last Published: October 30, 2015ArcGIS for Desktop
Bug ID Number
October 16, 2015
November 24, 2020
ArcGIS for Desktop
Operating System Version
After review by the development team, it has been determined that this issue is related to a known limitation with the software that lies outside of Esri's control. The issue's Additional Information section may contain further explanation.
This is as designed. The start end point of features is not guaranteed to be carried through to the output, and for M/Z attributes the first feature attribute found for intersecting vertices is used (in this case, 0).
As a workaround, the Pro only tool PairwiseIntersect will return what you are looking for in this case. The output created by the PairwiseIntersect tool can be quite different than the output of the Analysis Intersect tool so be sure that changing to use the PairwiseIntersect tool is appropriate for your analysis.