The Hollow Needle is found at the end of the Cellar Archives, while escaping from the Kaernk. The door to the next area in the game, the Archive Tunnels, is locked. This door can only be unlocked by the Hollow Needle.
Later on in the game, the player must find the Copper Tube in the Morgue. The Copper Tube and Hollow Needle must be combined to make a makeshift syringe. The syringe must be placed in a dead man's corpse's head in the Morgue, to allow blood to flow out of it. You can simply combine the items in the inventory or put the Copper Tube in the head followed by the Hollow Needle to get the syringe. While the blood is flowing, the player must utilize this opportunity to inject one's self with the blood, which is a vaccination that allows the player to get through fungi gas-ridden areas with ease.
Once the syringe is placed in the corpse's head and used to inject once, it has no further use and is left there.