The process you are describing is called osmosis. Osmosis is diffusion by water and it is a process cells use to equalize water content both inside and outside the cell.
A great example I used in my class room was to take a chicken egg and soak it overnight in vinegar. The vinegar dissolved the calcium in the eggshell, the result was a soft, pliable, somewhat transparent version of the egg within it's cell membrane. The next step involved immersing the egg in a beaker half full of Karo table syrup, which has a low water content. The egg soaked another 24 hours in the syrup.
The next day, I pulled the egg out of the syrup. The students were amazed to see it had a "deflated" appearance, because a large portion of the water within the egg had diffused across the cell membrane into the syrup, in an attempt to equalize the water content of the syrup.
I then put the now deflated egg into another beaker, and this time filled it with water. We let the egg set another 24 hours. The next day, when I pulled the egg out, it was back to it's original appearance because the water from the beaker had diffused across the cell membrane in an attempt to equalize the water concentration inside the egg.