I'd venture to say one of the lead wires is broken just inside the case or where the lead wire is soldered to the magnet wire internally. It's very rare for there to be an open magnet wire in the stator core. You'll usually get a shorted turn or a short to case if the the motor has been overheated.
This former is likely fixable. When you take the motor apart, be careful not to chip any of the magnets. Some suitable shim stock inserted between the rotor and stator will help prevent this.
If the problem isn't a broken connection just get a new motor. Most stepper motors follow a standard NEMA or ISO form factor so a drop in replacement should be relatively easy to find.
Why throw it out? Here's why: Rewinding a stepper motor is not trivial and WAY more complicated than rewinding a typical induction, 3-phase or DC brush motor. PLus, you'll likely find a suitable replacement for not a lot of dough.
Basically it involves winding the correct number of turns on a specific number of coils (one coil for each slot in the motor's stator) of the right gauge wire on what's called a stack fixture. The stack is basically a bunch of discs and bushings. Each disc has a small groove in the OD to allow the wire to pass across the disc for the next coil. Between each disc, a coil for each slot is wound.
When you've wound all of the coils, the stack assembly is taken apart, leaving you with several individual coils connected by a wire. Picture a bunch of cursive 'o's strung together. Except, of course, each 'o' has many turns.
This coil set is then inserted into the stator's lamination stack one coil at a time. Since you have an 8 wire motor, you'd have to wind and insert 200 coils (if it's a 1.8 degree stepper) and install them into 50 slots. Then the finished stator needs to be impregnated with a resin to prevent the wires from rubbing against each other (because of the Lorentz force).
John