I'm looking for a type of plastic membrane that would let water through it from the outside, but wouldn't allow water to escape once it's inside the membrane.
Ideally available in a roll.
Does such a plastic membrane exist?
The comments above have gently hinted that it would be a violation of thermodynamics for a passive membrane to force a substance in a single direction. Molecules have an equal probability of moving through the membrane in either direction, unless you apply a force to make them move in a specific direction, such as electro-osmosis or active water transport in plants.
Consider that if such a membrane as you posit existed, you could use it to pump water from a lower level to a higher, and then power a water-wheel: perpetual motion. Sadly, Maxwell's demon is getting a bit arthritic to shuttle water molecules, and the dampness only aggravates its condition.