Even patients with bad central DI can usually keep up with themselves if they have unrestricted access to hypotonic fluids, even without dDAVP. In the correct dosing, dDAVP fixes the problem and normalizes urine output and free water content. We usually try to under-dose them a little to prevent an SIADH situation from developing.
Central DI in patients without intact thirst is a challenge. In the neuroICU, patients with severe ICP elevations or post-op pituitary tumors are the usual culprits. You have to take over both their free water and salt maintenance, which is hard. People in florid DI make liters of urine an hour, and you can put them into circulatory collapse if you don't keep up with them. You treat them by putting back what they put out, and since they are making very dilute urine (usually specific gravity < 1.005), then you give them back D5W. Of course, you need to get them on a dDAVP regimen as well, and the dosing can be tricky. Blood loss, fever, diarrhea, etc. are also going on in the background, making it very difficult to assess and maintain appropriate volume status. Salt and water are intimately related, and once one of them gets off relative to the other, it can be tough to fix.
You can quickly correct sodium on a hyponatremic or hypernatremic patient if they developed the situation quickly. The reason is that the brain requires time (many hours to days) to normalize cellular water. Acute hyponatremia causes cerebral edema, and chronically the cells decrease the amount of idiogenic osmoles to circumvent this. Correction too quickly in a chronically hyponatremic patient can cause myelinolysis, classically pontine but it can happen in other places too. In a hypernatremic patient, the situation is different in that loss of cellular water essentially shrinks the brain. To try to counteract this chronically, the brain cells increase idiogenic osmoles to try to recruit water back. If you then suddenly drop the sodium, the brain tissue sees a huge osmotic gradient and swells, creating cerebral edema.
Classic example, and one that we do see, is marathon runners who drink only water during the race. They lose a ton of salt in their sweat and don't eat enough to replace it, and they drink only water which exacerbates the problem. They then pass out and seize, and come into the ED with a sodium of 115. Their problem is cerebral edema, and you want to fix it ASAP before they herniate and die. So you give them 23% saline boluses (30mL) and start them on a brisk 3% sodium chloride infusion. Mannitol would work too to decrease the edema, but they are likely volume depleted already, and you risk making that worse. The sooner you fix their sodium, the sooner they get better.