Unrouted wires double after routing in eagle
Some CAD packages that save their native database in a binary format can develop internal database errors due to strange corner case software bugs. I've had experience that sometimes this can be worked around by exporting the design to an ASCII format. Then close and re-open the CAD tool and import the ASCII format database into a new design file. 

Surprisingly I had a problem very similar to the one you are describing here in a design some 12 years ago that required the "fix" I describe above. That was with PADS software.