Why is there water in my washing machine barrel some time after a load?
It sounds like you have something causing drain water to backup, and siphon back into the barrel slowly.  The drain pipe that runs to the utility sink... does the pipe incline to get to the sink?

I had one many years ago and I can see it in my head.. the pipe would hold about 1.5 gallons of water, and would stink quite badly.  I never had it run back into my machine, but it would occasionally get knocked off the sink and spill on the basement floor.