It depends where this choking of the traces is on the board. If the washing is one of the newer models it probably has a brushless DC motor.
You can see if the machine has brushless motor by looking at the number of wires going to the motor. A brushless motor will usually have 3 wires for the phases and most likely one for protective ground.
If the choking is on the power going to the transistors (usually on the low side of each half bridge) or on the lines going to the motor they could be used as series resistors to measure motor phase currents.
In the new washing machine models they use what is called field oriented motor control to minimize vibration and for load compensation.
If those are used for current measurement and they are blown most likely there is short somewhere or the motor itself is gone. If they are on the low side of the half bridge you will probably have a blown transistor and if they are in series with the motor than you guessed it, it is most likely the motor.
They do that so the thin trace acts as a fuse. Use a single strand out of some 20AWG cable as a replacement, soldering to the pads on each side. There probably were provisions made on the top of the board for 2 solder in fuses in this design.
I don't see any good reason for any PCB designer to make a fuse as a track as it will be hard also for the manufacturer to fix (when still in warranty).