Do washing-machines provide a AC connector which is live when the machine is working?
No, they don't generally have such an outlet.

Perhaps you are looking for an Automatic Washing Machine Shutoff Valve? These devices sense when the washing machine is using electricity and open the water supply valves. Once the machine stops using electricity (i.e., the cycle is done) then the valves shut. Many models also include additional features such as water sensors for the floor, and timers that close the valve after x minutes even if the washing machine is still pulling current.