- You may be looking for the spatial end of the universe.
The end of the universe was an event that took place far off into the future in which the universe, or N-Space, collapsed in on itself due to being a closed system and entropy constantly building up. It was also known as "Event Two", (PROSE: The Infinity Doctors) the "Big Crunch" (PROSE: Timewyrm: Apocalypse, Millennial Rites, Sometime Never...) and the "Blue Shift". (PROSE: Timewyrm: Revelation, Do You Love Anyone Enough?)
Projected dates
Long before 1981, the universe had already passed the point of total collapse. Having discovered this, the Logopolitans created Charged Vacuum Emboitments which opened N-Space into other universes, notably E-Space, allowing entropy out of N-Space and into other universes. Though Logopolis was destroyed in 1981, a single CVE was rebooted and continued to feed entropy from N-Space into E-Space. (TV: Logopolis)
The end of the universe was projected to occur in varied times, including the years 60,000,000,000 AD (AUDIO: Zagreus), 100,000,000,000,000 AD (TV: Utopia) and, in an alternate universe, 100,000,000,000,000,000,000,000,000,000,000 (One hundred nonillion, 1032) AD. (PROSE: The Infinity Doctors)
The Mandelbrot Set informed the Grey Man and Bernice Summerfield that, due to the actions of Gabriel and Tanith in 1994, the universe would now end "several metacenturies" earlier than projected. (PROSE: Falls the Shadow)
Attempts to end the universe
In 1981, the Tremas Master nearly ended the universe when he disrupted the Logopolitans' Block Transfer Computations which closed the CVEs they created. As a result, an entropy wave formed which caused heat death as it spread through the universe. The Fourth Doctor prevented the total destruction of N-Space by reopening the last remaining CVE which dissipated this accumulated entropy by feeding it into E-Space. (TV: Logopolis)
Dimensional transference was a theoretical phenomenon caused by a black light explosion that would threaten the stability of the entire universe. Intrigued by the uniqueness of this, Drathro allowed his black light converter to fail before he was stopped by the Sixth Doctor. (TV: The Mysterious Planet)
Donna Noble prevented the Daleks from destroying the universe, indeed every universe, using their reality bomb (TV: Journey's End) The Tenth Doctor later stopped the Time Lords from transcending into creatures of pure consciousness, as a means of escaping the end of the universe they tried to cause. (TV: The End of Time)
Actual ends
The total event collapse induced by the destruction of the Doctor's TARDIS. (TV: The Pandorica Opens)
The Kovarian Chapter of the Silence (TV: The Time of the Doctor) caused the universe to undergo total event collapse when they destroyed the Doctor's TARDIS, causing every star to explode at every moment in history. (TV: The Pandorica Opens) The Eleventh Doctor was able to "reboot" the universe using a restoration field. (TV: The Big Bang)
Species at the end
The Panjistri created the God Machine in an attempt to prevent the end of the universe. (PROSE: Timewyrm: Apocalypse)
The Divergence almost emerged into the universe at the end of time, but were defeated by Walton Winkle and the animatronic residents of Winkle's Wonderland, which had been built over the ruins of Rassilon's Foundry. (AUDIO: Zagreus)
The Ministers of Grace lived at the end of time. (PROSE: The Duke of Dominoes)
Most of the people of the universe were relocated to the Needle. The Emperor was ruler of the universe, but was assassinated. His daughter was taken to the 20th century and named Miranda Dawkins. (PROSE: Father Time) She later returned to her own time and became Empress. (COMIC: Miranda)
The planet Endpoint, inhabited by a human-descended species called Endpointers and ruled by Silver, a human from the year 3006, was visited by the Eighth Doctor. (PROSE: Hope)
The inhabitants of Ember attempted to survive the end by using the Somnus Foundation on 21st century Earth to transform humanity into a gestalt entity. They were defeated by the Fifth Doctor and Turlough. (AUDIO: Singularity)
The Toclafane emerge from the end of the universe in May 2008, starting the Year That Never Was. (TV: The Sound of Drums)
The Toclafane, with the aid of the Saxon Master, attempted to survive as well by travelling to 21st century Earth and murdering their ancestors. They were defeated by the Tenth Doctor and Martha Jones. (TV: The Sound of Drums/Last of the Time Lords)
The Council of Eight existed in the Vortex Palace at the end of time. (PROSE: Sometime Never...)
According to legend, the Sycorax would be one of the last three races left when the universe died. (COMIC: Agent Provocateur)
Bug-like creatures nicknamed bookworms fed on the debris at the Big Bang and the collapse of the universe. (COMIC: Hunger from the Ends of Time)
The Twelfth Doctor on Gallifrey at the end of the universe. (TV: Hell Bent)
The Time Lords existed at "the end of the universe, give or take a star system", having moved Gallifrey there for protection when they emerged from the pocket universe the Doctor had placed it in. Further on, at five minutes before "Hell", Me was found by the Twelfth Doctor, waiting in the Cloisters in the bowels of the Capitol for the end of the universe. In her own words, she had been watching the stars die to pass the time until the end. However, she eventually left with Clara Oswald to drop the Doctor off in Nevada, and then to take Clara back to Gallifrey "the long way round." (TV: Hell Bent)
Visiting the end
Numerous advanced civilisations used the end of the universe as a dumping ground for dangerous items. The Third Doctor took Sergeant Kandula's body and the Tipping Device to the end of the universe and left them there. (PROSE: Midnight in the Café of the Black Madonna)
The Fourth Doctor and Romana II watched the universe end from some unknown vantage point. As the dimensions collapsed, the Doctor gave Romana the last Rolo in the universe. (PROSE: Do You Love Anyone Enough?)
In an alternate universe, the Doctor escorted General Sontar and an ambassador of the Rutan Host to the far future, several years before the actual end, only to discover a lifeless grey void. (PROSE: The Infinity Doctors) Faction Paradox's The Book of Lies claimed a "greyness" would fall over the universe, and the Boy gleefully told this to the Eighth Doctor. (PROSE: Unnatural History) After the War, the Klade would accuse Miranda's father, the Emperor, and his kin of draining the universe of energy and bringing its end too early. (COMIC: Miranda)
River Song said that she and the Doctor had been to "end of the universe" together. (TV: Forest of the Dead)
During the Last Great Time War, to prevent the Time Lords from deploying the Tear of Isha into the Tantalus Eye, which would wipe out twelve planets in the Tantalus Spiral, the War Doctor hijacked Commander Partheus' TARDIS and travelled to the end of the universe. Cinder deployed the Tear into one of the last stars in existence, a red giant, and it collapsed, causing no harm to anyone. (PROSE: Engines of War)
Orson Pink was sent to the end of the universe after taking part in a 22nd century time travel experiment that sent him too far. The Twelfth Doctor found him trapped on the last planet in existence. (TV: Listen)
To purge his TARDIS of the Plant, the Twelfth Doctor brought it to a point in time after all stars had ceased to exist. The lack of solar radiation led to the Plant's death. (COMIC: Petals)
When the Doctor emerged from his confession dial on Gallifrey, (TV: Heaven Sent) he was at "the end of the universe, give or take a star system", Gallifrey having been moved there for its own protection. He later visited Me in the same location, five minutes to the end of the universe. She had been able to reside there through use of a reality bubble in a ruined section of the Cloisters from Gallifrey, where she watched the stars go out and found it to be both sad and beautiful. The Doctor and Ashildr left the bubble and returned to Gallifrey before the bubble gave out and the final remnants of the universe collapsed. (TV: Hell Bent)
Other information
The Black Guardian was most powerful at the end of the universe, where his counterpart, the White Guardian, could not interfere. (PROSE: The Well-Mannered War)
River Song noted a theory for the SporeShips' origin, that they slipped back in time from the end of the universe as an example of a time paradox. (AUDIO: Signs)