Should be an easy fix. If you machine will shut off the water when you stop it, then the problem is likely in the tube that runs from the tub to the water level pressure switch. This switch is air pressure operated, and triggered by high pressure that occurs when water fills up the tube and causes the switch to tell the timer to shut off the water.

Take off the cabinet, instructions here,

Kenmore top loader blues (SublimeMasterJW's Appliance Advice)

and clean out the tube that goes from the tub to the switch. If that does not fix things, you will need to change out the water pressure switch.

If the water does not shut off when power is shut off to the machine you will need to replace the water valve assembly. It is also accessible by taking off the cabinet.