Have you measured the resistance across the coil to confirm it is broken? If it is, then you might be lucky enough to find the break and solder in a bit of new wire. However that is probably hoping too much as the wire has enamel on it to stop it shorting to the other strands next to it, and if it got hot enough to brake, then the enamel around that wire and others near it will also be melted. You will have a number of shorted turns. Anyway you might manage a repair but most likely to need a replacement.

... if you do, can I have the broken motor?