It is important to note that sudden restoration of blood volume to normal will turn off the stimulus for continued ADH secretion.
This can cause a sudden and dramatic increase in the serum sodium concentration and place the patient at risk for so-called "central pontine myelinolysis" (CPM).
As a result, the kidneys of such patients recover water and produce a fairly concentrated urine.
Treatment is simple (if not without risk) — simply restore the patient's blood volume, thereby turning off the stimulus for ongoing ADH release and water retention.
Patients taking diuretic medications such as furosemide (Lasix), hydrochlorothiazide, chlorthalidone, etc., become volume depleted.
As mentioned above, lack of adequate blood volume is a potent stimulus for ADH secretion and thence water retention.
Treatment of these patients involves treating the underlying disease that caused the fluid to leak out of the circulation in the first place.