Drain valve will not close after power is off to the selenoid.
Did you measure it with a meter?
On most GE's the solenoid only gets power for about 5 seconds and then the water pressure holds the flapper valve close till the tub is empty.

Is the motor supposed to shut off to allow this to happen at the end of drain cycle?
Cannot say for sure on this specific Model but on most units the pump does not have to shut off.
Could be that the unit is not emptying correctly.
Possible causes are a partial drain clog, a bad drain pump, debris in the sump or a bad Piston and Nut.
When you open the door is all the water out of the unit?
Note that it is normal for these units to leave about 1/4 inch of water in the tub as the pump seals will burn up if run when the sump is dry.