the wrapper does looks a little toasty but the coil may be ok ( when removed check with an ohm meter)

The coil sleeve is probably what pieces are falling out, order a new one of those as well

You will want to clean the whole stepper unit so things work smoothly

Part catalog here: http://www.planetarypinball.com/reference/partsmanuals/BLY_Parts_1976/index.html#/106/

Some great info here about working on EM games: http://www.pinrepair.com/em/

I have ordered from Steve Young at The Pinball Resource: http://www.pbresource.com/coils.html can call him on the phone and ask for the correct coil sleeve as well as the coil part # given above.