As Graham said above, the instrument has two mechanisms within.
Your speedo works so the problem is not the drive cable, nor the speedometer itself.

The odometer is gear driven. The drive cable turns a worm screw which turns a toothed gear. This gear is directly attached to a pawl via an eccentric pivot. Every turn of the gear will pull the pawl once. The pawl turns a plastic (coloured) gear at the end of the odometer wheels.
Everything up to the pawl is pretty robust, mechanically linked and unlikely to be the problem.
Everything away from the coloured gear in the odometer drums is equally robust.
The most fragile element is the pawl and/ or the gear wheel it drives.
i.e
1- The plastic tooth gear can be stripped, or the clip that holds the pawl to the eccentric pivot may have fallen off allowing the pawl to fall from the eccentric.
2 -The spring pulling the pawl to the gear on the wheels may be weak or missing. This may prevent the pawl from touching the gear and thereby prevent any motion of the wheels.
If the odometer is exactly at 50,000 the gear train will have had to push all 5 of the barrels to get from 49,999 and this may have been too much effort for the pawl or the spring.
My suggestion would be to have a look and see for yourself:
- disconnect the cable drive, remove the bulbs and take the instrument out. Once out; an 1/8th of a turn of the bezel should release it and the glass. Two through screws retain the mechanism and face to the back of the case, remove these and the innards will ‘fall’ out as a complete mechanism.
At this stage, the condition of the pawl, spring and drive should be asertainable and will tell you what to do next. If the above are OK all that may be necessary is a number of nudges to get you away from 50,000.
DON’T go further and think it would be ‘fun’ to correct the mileage drums!
Reassembly is as Mr Haynes would say is in the reverse order.