Software viruses that do not replicate, but can damage the computer by opening doors for hackers to enter the computer are known as a Trojan horse.
If you know Greek history well, this answer should be obvious. Allegedly, Greek soldiers gave Trojans a large wooden horse as a gift, however, they hid in it and killed many Trojans during the night. This is similar in computer terminology - the virus infects your computer without actually damaging it, but rather stealthily provides access to hackers.
