Will water that contains no solute ever stop flowing into a hypertonic solution through osmosis?

No, it will never stop flowing

Explanation:

Osmosis is the movement of water from an area of lower concentration of solute to an area of higher solute concentration through a semi-permeable membrane. If one side of the membrane is completely free of solute, water will move to the hypertonic solution continuously in a bid to achieve equilibrium until all the water completely moves to the hypertonic side. This is because equilibrium cannot be attained since one side is completely void of solute and another has solutes.

It is like having red coloured paint on one side and water on another side of a membrane, and the water moves into the paint compartment and only stops when they both have the same color. No matter how much water moves across, they cannot have the same color on both sides.