The sprockets on some machines have a hub welded to the center that is splined or keyed onto the axel. I believe these are the welds that fail. I don't know if you would have enough room to weld it in place. Also you would have to be careful about cleaning out the chain case and not roting your ground through a bearing.
Will you wheels tun if you jack the machine off the gound or not at all?
Also does the motor labour when trying to turn them. Pump or hyd motor failure is a more common reason o have both wheelson the same side stop working.
For it to be a mechanical breakage, it would have to be the sprocket on the motor, not the axel, because a axel sprocket would only stop either the front OR rear wheel on that side , not both.
Ken