important thing. There shouldn't be any water on the floor and the drain is for emergencies only.

If the valve in the washer is malfunctioning, then fix the valve and put in a drain pan so if it happens in the future your floor is not at all affected. I would guess that the floor drain is not connected to your sewer system, unless there's a p-trap in the floor to keep the sewer smells from coming up. Since there should never be water in a floor drain under your W/D, there would never be water in your trap sealing the smells. Often, drains like this are just routed to the exterior with a 90 degree turn down pipe fitting on the end to get the flooding water out of the house. If this is the case, then no water can back up through that floor drain. When I built my home, I routed these emergency drain lines to terminate above a window so I would notice if there is water coming out of them.

If the leak is in the wall, or coming up through the actual washer drain in the wall, then you've got a bigger issue.

First thing, recreate how the water got on the floor to begin with.

I've had friends that have lost their floors and had extensive damage due to a $2.00 plastic valve inside the washing machine fail. It's constantly under pressure and opens and closes with the wash cycle. Due to this, I have one lever shutoffs at my washing machine hookups and flip them both off when I leave town.