If the cell membrane becomes totally impermeable, water and dissolved gases, most notably oxygen, would no longer be able to enter or leave the cell. The cell membrane is usually permeable to a number of substances, mostly small, nonpolar molecules. Other polar or charged particles are transported across the membrane by special embedded protein structures, and so would not be directly affected by a change in membrane permeability.
The membrane permeability of animal cells and many other organisms is crucial to their survival. The inability to absorb oxygen or release carbon dioxide would quickly be lethal to such organisms. However, other organisms less dependent on oxygen-based metabolism would survive a while longer, although the condition would eventually kill them as well. One example is yeast, which takes in food molecules and generates energy from them without the need for oxygen.
The ability for water to pass through cell membranes is often as much a hindrance to the cell as it is a benefit. Many cells, particularly single-celled organisms, exist in environments with a different amount of solute in the water outside than they have inside. Thus, water tends to move into or out of the cell constantly, which the cell compensates for by expending energy.