I have a top loading washer and the last time I put clothes in to wash, the water started "filling" the tub right away, so I went upstairs to bed. In the morning, the water was still "filling". The timer did not turn it off after the timed cycle. There was some water on the floor, but not over 8 hours worth... so, the majority of it must have gone out of the drain hose. The next time I checked it, it did the same thing. The pump was not going to empty the tub, it just would not fill.

You are blessed that it did go down the drain mostly. I had this happen with a Speed Queen when I lived in an upstairs apt. after I went to bed - cost me a lot of money for the water damage below me.

I presume the washer was functioning OK prior to this, or is this is a new location / install for the washer? If new location - make sure your standing drain pipe is high enough per the washers instructions. If the pipe is too low, the water will siphon out, and never really fill up.
If the pipe is the right height, then you have a pressure switch acting up. If it is the pressure switch - again, you are blessed. I really don't know why you did not have a flood.

I have a top loading washer and the last time I put clothes in to wash, the water started "filling" the tub right away, so I went upstairs to bed. In the morning, the water was still "filling". The timer did not turn it off after the timed cycle. There was some water on the floor, but not over 8 hours worth...so, the majority of it must have gone out of the drain hose. The next time I checked it, it did the same thing. The pump was not going to empty the tub, it just would not fill.
There's aproblem with your timer... call a technician

There's aproblem with your timer....call a technician
Probably right.

NO, the problem is NOT with the timer! Neos is correct in his first assumption, that the drain hose is probably not high enough and the water runs into the tub but then right out again. Raise the drain hose and it will cure the problem, 95% sure of it. :)
In the remote chance that the end of the hose is stuck really tight into a stand pipe and sometimes people will even put tape around the pipe and drain hose, syphoning action will also cause a similar problem, 5%.:p