Considering that the brine output of a single large-ish plant might be 150,000m³ per day[1], that's a hell of a mine shaft to take it continuously. The rock with the same volume as a day's brine would weigh a million tons. The entire Aberfan spoil tips were only 2 weeks worth of that much volume (2 million cubic metres).
The gigantic Hambach open-pit mine grows by 0.3km³ a year, so that could take it (but it can't take the Saudi million m³/day plant). By the time the mine is depleted, the resulting 18km³ pit would not be filled by our single hypothetical plant for over 300 years, assuming it won't evaporate. Which leads to:
The evaporation pools might work: they'd "only" have to be 3000 acres (12 km²) to gather the 4GW of solar power at 1kW/m² for 8 hours a day to continuously evaporate that much water daily[2]. Which is certainly large, but not completely impossible. But then there's 2 million tonnes of salt per year which will accumulate continuously over time.
[1] the largest is over a million
[2] not including water not bring a perfect absorber of solar energy or differing insolation
