Digimon Story: Cyber Sleuth

Players assume the role of either Takumi Aiba or Ami Aiba, male and female Japanese amateur hackers. They receive a device called a Digimon Capture from a mysterious stranger in a chat room which allows them to capture and befriend Digimon, creatures who inhabit a next-generation version of the internet called Cyberspace Eden which users can physically enter. After traveling to the lowest levels of Eden, they are attacked by a data-based entity called an "Eater" who leaves their bodies half-digitized, and find that they can now freely travel between the real world and the virtual world via terminals.

Source: Wikipedia, "Digimon Story: Cyber Sleuth", available under the CC-BY-SA License.