It is unknown where the Drashigs actually come from.
The Drashigs are like worms but are carnivores and are blind. They hunt using smell and can follow anything that they can smell. We saw some Drashigs inside a miniscope which was banned by the Time Lords because of the miniaturising of creatures who you can store in it. The Drashigs weren't the only creatures inside the machine there were also humans, a Cybermen, Ogrons and even a Plesiosaurus. When the Doctor and Jo got into a swamp like area they saw the Drashigs jumping out of the ground. When they ran away from them, one of the Drashigs chased them using their scent. The Drashig even broke through the area and into the controls of the machine.
The Drashig chased the Doctor and Jo onto a ship which was suppose to vanish. The Drashig scared a lot of the humans and then all the Drashigs were emerging out of their home. The Doctor and Jo managed to escape the Drashigs but two of the Minorians let the Drashigs out of the scope. The Drashigs go back to their original sizes and terrifies everybody. The owner of the machine Vorg kills the Drashigs using an eradicator machine. The Drashigs and the miniscope were destroyed. All of the creatures were returned to their own times.
The Drashigs appeared in:
Season 10: Carnival of Monsters