In one timeline, the Valeyard succeeded in killing the Doctor in the Matrix, gaining his knowledge and obtaining immortality. He created Chronopolis, a city within the Time Vortex around his TARDIS, which protected it from harm. The Valeyard placed a sample of every extinct species within it. Initially the Time Lords were willing to let the Valeyard exist as an object of potential study, some believing that his lack of morality would make him a more effective "agent" than the Doctor, but his obvious interest in chaos for its own sake - equally willing to avert the creation of the Daleks and have humanity make contact with the Silurians as to leave Earth at the mercy of the Vervoids - eventually forced the Time Lords to recognise the dangers of letting the Valeyard roam free, albeit too late to stop him recovering the Doomsday Weapon and turning it on Kasterborous.
However, a great deal of this was an illusion: the Valeyard had travelled in time and interfered so much in the lives of his past selves that he had radically damaged Time, ranging from accidentally destroying the Fourth Doctor's TARDIS on the way to Logopolis to planning to kill Dodo Chaplet to stop the Doctor's first visit to Logopolis. Eventually, he was left hiding in his TARDIS, which had generated various force-fields to keep him immobilised, the Valeyard now terrified to take any action lest he make things worse. The TARDIS generated the fantasy of Chronopolis to make the Valeyard feel safe. Mel became trapped with him while trying to bring the Doctor out, and the two were frozen in Time, possibly forever, as the universe waited to heal, the TARDIS's power becoming so drained that it was forced to turn the force-fields to full power rather than spare the energy to let them talk. Ultimately, the Valeyard gained respect for the Doctor at this terrible end, referring to his greater wisdom and experience, recognising that the Doctor sometimes avoided taking action because it was more practical rather than because he was afraid. Furthermore the Valeyard finally saw the damage his actions had done, using his last words before being frozen to apologise to Mel for everything he had done. (AUDIO: He Jests at Scars...)