Apparently, the Dead Sea has no outlet. It’s the end point of the River Jordan, the source of which is in the Golan Heights on the border between Israel and Syria.
The river runs from the Golan, through the sea of Galilee (which is a lake, and is known as the Kineret in Hebrew), and onwards south to the Dead Sea.
So why doesn’t the Dead Sea fill up?
Perhaps its rate of evaporation is greater than the rate at which water flows in? After all, it is very saline, so there must be considerable evaporation. Still, with water flowing in all the time, it surprises me.