The best situation I can imagine is feeling dull-witted or terribly weak after days of sweating
Under the right conditions (usually found in desert and jungle areas) the onset of unconsciousness from sodium chloride depletion can be measured in hours not days.
The temperatures in these places force you to drink large quantities of water which if not balanced with salts dilute the sodium chloride levels in the blood to dangerous levels.
There is a recorded case (which frustratingly I cannot find my papers on now) of a girl collapsing and dieing of heat stroke in the jungle on a British expedition company excursion.
She had arrived in Singapore and traveled into the jungle the day before, she complained of a headache and was found to be dehydrated so was given water to drink, a hours later she fell unconscious and stopped breathing, an immediate evacuation plan was put into action but the only I.V. needle in the medical kit broke so they were unable to deliver fluids (part of the medical kit had gone with a person evacuated earlier after sustaining a suspected fracture) it took all night to evacuate the girl with continuous artificial respiration the whole way, but the did not recover.
Investigation into this death found that she had been taken the advice to drink lots of water and had done so, however it was discovered that she was on a low salt diet and so had been avoiding all salt.
in this country we are quite versed in the dangers of hypothermia but very ignorant of the great danger posed by hyperthermia
you are correct that salt tablets are not recommended though, salt should be taken on food or in an electrolyte drink.