Reach inside to the broken off end and scrape away the enamel insulation from the broken wire end with an xacto knife. If possible, get the tips of a curved pair of surgical forceps in there and form a tiny hook in the wire end. Make a similar hook in the end of the wire you will connect to it. If space permits, hook them together and then squash them together with the forceps. if not, you will just have to hold the wire in place during soldering.
You will find you can slip a couple of thicknesses of vinyl tape under the windings from the side -- the windings are slightly raised above the field core. The tape will serve as insulation between the solder joint you are about to make, and the field core.
Solder the two wires together with a blob of solder. This may take a couple of tries and a little drop of flux paste may help.
Try to anchor the new wire in the fiber plate on the field end by using an existing hole or drilling a new one. This is to act as a strain relief so the new joint, which isn't that strong, won't get tugged apart. Tape two or three turns thru the hole.
I have performed this operation many times. If you are careful, do good work, and anchor the new wire well, you will end up with a good running loco.