This is a hyponatremia in which the normal mechanisms of water resorption and sodium retention have failed.
The usual causes of this state are damaged kidneys, which make no effort to reabsorb sodium, and which fail to respond normally to ADH. Thus sodium excretion continues in spite of low sodium, and the urine remains dilute in spite of the fact that there may be hypovolemia.
In acute renal failure, the urine osmolality is unpredictable. A combination of tubule dysfunction and reduced urine delivery to the distal nephron reduces its ability to reclaim sodium from the tubular lumen; additionally the ability to concentrate urine (i.e. ADH responsiveness of the collecting duct) may be lost. There may be a few tubules still receiving fluid, and they will suffer from a combination of sodium resorption failure and ADH unresponsiveness, thus producing a relatively low volume of dilute, sodium-rich fluid.
In contrast, in chronic renal failure, the urine osmolality trends towards about 300mOsm/Kg ("isosthenuria"). Water intake in these patients is not matched by excretion, and a dilutional hyponatremia develops; the sodium loss occurs because of insufficient efforts to reclaim it from the tubules.
Having had your urinary outflow tract clogged has the result of damaging tubules by direct back-pressure. Pressure back into the glomerulus prevents normal glomerular filtration, and fluid which would have otherwise been filtered passes through the kidney without ever encountering the tubular lumen. Urea builds up as a result.
During the obstructed period, it seems numerous diuretic factors are released, and their effect becomes evident after the obstruction is released. The effect is that of proximal tubule dysfunction; massive dilute diuresis and uncontrollable sodium excretion ensue. The pent-up serum urea is now free to escape via the glomerulus, and it also acts as an osmotic diuretic, increasing urine volume and maintaining urine osmolality somewhat above the "maximal" dilution.
Additonally, it seems the Na+/K+ ATPase in the distal tubule stops working; if the sodium is not being pumped out of the cell effectively, no gradient for sodium reabsorption can be maintained, and consequently sodium and water are not reabsorbed.
Sodium transport in the proximal tubule relies on the action of Na+/K+ ATPase sucking sodium out of the cell (and into the peritubular capillary), maintaining a gradient to drive the Na+/H+ antiporter which gets sodium out of the tubular lumen. Obviously, this is a hungry process. It demands vast quantities of ATP. In a state of ischaemia, this process breaks down, and sodium remains in the proximal tubule lumen. Seeing as about 85% of sodium resorption occurs here, one might expect a significant resorption problem to occur in acute tubular necrosis.
Indeed it does occur. With sodium transport in the tubules being such an energy-intensive process, one cannot expect the war-ravaged post-necrosis tubules to squander their scarce resources on moving ions back and forth. They are too busy healing. Furthermore, they are resistant to aldosterone and ADH. The result is a failure to reabsorb the sodium as it travels down the tubule, as well as a failure to reabsorb water. Once the glomerulus recovers, it sends a normal amount of fluid through the tubule, but the tubule simply doesn't care.
The resulting urine is likely to be reasonably dilute (above 100mOsm/Kg is still quite dilute) but with an abnormally high urinary sodium. Replacement with normal saline seems to be the treatment of choice.
Weirdly, one cannot find any good data in the literature to discuss this process. textbooks discuss acute renal failure and ATN, throw away a line about how glomerular filtration normalises but tubular resorption doesn't, and then they move on. It is possible that nobody has a good handle on what precisely happens here.