The Slavers originate from Larry Niven's Known Space universe. In Niven's other works, the true name of the Slavers is the Thrintun (singular Thrint). The Thrintun ruled the galaxy through telepathic mind-control in the distant past. They are a carnivorous species with an uncontrollable hunger and low intelligence. Their dominance over other people is derived solely from "The Power", their telepathic abilities that can turn any intelligent beings into slaves.
About two billion years before Humans emerged, the Thrint were nearly destroyed by one of their enslaved races, the Tnuctip. In reaction, the Slavers issued a universal "Die!" command, causing every sentient being in the galaxy to kill itself in an event known as Suicide Night.
In the Star Trek universe, this total extinction of life in the Milky Way Galaxy may have left some survivors, as the Taguans are said be have had a continuous history dating back two billion years. (TNG: "Qpid") It's also known that the Q were active around this timeframe, though the Q Continuum's extradimensional existence and abilities may quite possibly have protected them.
The depiction of the Slaver in "The Slaver Weapon" follows the physical description of the Slavers in Niven's works quite closely.