The cells will shrink because water will leave them to equilibrate the osmolality. Occasionally, this is useful.
The cells will secrete new osmotically active substances ("idiogenic osmoles") to counteract this fluid shift.
The production of idiogenic osmoles can also be downregulated to adjust for chronic hypotonic states
Neurons are notorious for this activity. This the mechanism of coping with chronic hyponatremia: the drop in serum tonicity causes the neurons to swell, which then causes the neurons to downregulate their idiogenic osmole production, and thus to compensate for the drop in ECF tonicity with a drop in intracellular tonicity.