Chrome extension Trojan tricks victims in an endless malware loop

Most trojans come in two parts, a Client, and a Server, but there are exceptions where the trojan does not need a Client, as it's able to automatically do what it was intended to do (stealing passwords, business data etc.), without any intervention from the attacker.

They are,
Remote Access Trojans (RAT's)
Password Sending Trojans
Keyloggers
Proxy/Wingate Trojans
DeDenial Of Service (DoS) Attack Trojans
FTP Trojans
structive
Software Detection Killers

A Trojan can have one or multiple destructive uses—that is what makes them so dangerous. It's also important to realize that unlike viruses, Trojans are not self-replicating and are only spread by users who mistakenly download them, usually from an email attachment or by visiting an infected site.

A destructive program that masquerades as a benign application. Unlike viruses, Trojan horses do not replicate themselves but they can be just as destructive. One of the most insidious types of Trojan horse is a program that claims to rid your computer of viruses but instead introduces viruses onto your computer.

Trojan horses masquerade as harmless programs, but when activated, they damage their host computer. Unlike a virus, a Trojan horse does not replicate itself; instead, this malware usually attempts to steal files or passwords. Computer worms replicate themselves to spread through a network.