Kenmore washing machine keeps filling and won't start
Kenmore model 11020022014 keeps filling with water and won't stop
Don't know too much about washing machines but I thought that this may be of some help to you.
Logically you would think that your problem may be with the water level pressure switch hose, the water level pressure switch or perhaps the electronic control board. Reluctant to say it may be the water inlet valve as you would think that if it didn't close to shut off the water that the water would be entering the machine all the time, but you never know.
Given the price of the replacement parts I am loathe to say which one may be causing the problem. If you are handy with a multimeter you may be able to verify electrically that the water level pressure switch is operating and sending a signal to the control board for instance, but be aware that there are lethal voltages present so if in doubt, DON'T.
Here is a link to the available spares for your model. It is interesting that it doesn't list a water level pressure switch, but I think it shows in the parts diagram, a combined water temperature / level pressure switch. I may be wrong about this of course, so if you do manage to prove the level switch? to be the problem you may have to ring the phone number listed to get more information, (scroll to the bottom of the page in the link).