Tub is filling with water, when the washer is not running.

Question edited for clarity. 'field cycle' to fill cycle.

Do you hear water running? Water inlet valve failed.

or

Taking too long to fill. Check the strainers in the rear where the hose connects and check water flow from the hose.

Also try a power disconnect overnight to do a power reset of the control board.

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If the cold water supply is slow or not entering the tub at all, the washer will stop ahead of the rinse cycle while waiting for the tub to fill. This can be caused by a clogged water inlet valve, the main water supply valve being partially closed, or low water supply pressure from the home.

Crosley Washer stops mid cycle - Repair Clinic

https://www.google.com/search?q=Crosley+Professional+Washer+washer+stopping+at+beginning+of+fill+cycle

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Hi,
Its sounds like you have a siphon going on, this happens when the drain hose it too low during fill and as the water enters the unit it exits through the drain hose. To stop this the drain hose needs to be higher than the tub itself, meaning: raise the drain hose behind the washer to about control panel area. This will or should stop the siphon effect and allow the water to remain in the tub. If the drain hose is low this siphon will start again.
I hope this helps

I’m happy to help further over the phone at https://www.6ya.com/expert/gere_bf68e6055dd61249

The problem is simple and easy to fix. Your washer has a tubing which runs from the base of the tub to the water pressure switch. It might have vibrated loose from the switch, or their can be some sediment in the tub. Blow out the tubing and reattach it securely to the switch and pump out the water in the tub. Then try it again. I wrote an article about this:
Help my washer is overflowing !!!

If you need further help, reach me via phone at https://www.6ya.com/expert/dan_73bbd84fe1d95b61

You need to check drain hose, the drain hose needs to be above the tub. If it isn't the water will just drain out when you fill

The water-level switch regulates your washer's fill volume. This switch is usually a diaphragm device with a small, clear tube attached between the switch and the bottom of the washer's outer tub. As the water level in the tub increases, the pressure on the air in the tube increases. When the pressure reaches a certain level, it activates the switch, shuts off the water, and signals the timer to begin the agitate cycle. If the switch is defective, it may prematurely signal the water to shut off. If so, you probably need to replace the water-level switch.

This machine has a water valve that works on vaccuum from the tub. You will see a small clear hose that runs from the side of the tub up to this valve. This valve is adjustable to change the water level in the tub to desired setting on some machines, but if it goes bad, it will not shut off, thus overflowing the tub. Find this valve and replace it if adjustment does not work.

be sure your drain is nearly to the top of the washer if it is you may need to try a siphon break

You need a new cold inlet valve fitting.

Check the hose from the tub to the pressure switch, make sure its clear and the reservoir on the tub is clean.

water level switch