Cold water pours in during final spin

I have a Kenmore stacked washer/dryer combo model number 417.98702891 (not sure of the year). When I run it through the regular cycle with the water set to Hot/Cold, it works perfectly. When I run the same cycle on Cold/Cold, it doesn't. It will fill and drain fine, spins at full speed, and the water shuts off when it is full.

The problem is that the final part of the cycle, the spin, it will pour water out while spinning thus making the clothes wet when it is done (occasionally the tub will be partially full at the end of the cycle). If I switch the water from Cold/Cold to Hot/Cold during this final spin, the water will turn off and it will function normally. It does this for all cycle settings.

At first I suspected the timer was bad, but I now suspect it is the cold water inlet valve. However, if it is the cold water inlet valve, why would it work fine throughout the cycle except during the final spin?