Careless digitising, importing from other GIS and automated cleaning of your data can sometimes introduce errors such as collapsing the geometry of a polyline into "nothing".   Such features still remain in your data and quite possibly retain their attributes. 

As these features take no part in a network should they be removed?  This depends if the connectivity of the network is broken. 

Experience has shown that null length polylines often have other polylines in "their place".  Removing the null length polyline will not break the connectivity of the network, so it would be OK to delete these if the attribute information associated with it was not important. 

If there is a visible break within the network and it is attributed to the null length polyline then you should rebuild the connectivity of the network by digitising the polyline.  You could delete the feature and start again or attempt to modify it which would retain it's original position in your dataset. 

This tool generates an error log file called NullPolylines.txt