The homeless were people so poor that they didn't have homes. Homeless people were sometimes called tramps.
During the Great Depression, many homeless people in America lived in shanty towns called Hoovervilles. In 1930, Hooverville residents in New York City were abducted by the Cult of Skaro and converted into pig slaves. (TV: Daleks in Manhattan / Evolution of the Daleks)
During the Blitz, many children were left orphaned and homeless in London. Nancy looked after them and helped them get food. (TV: The Empty Child / The Doctor Dances)
In 1966, a tramp was killed by labourers under WOTAN's control after he discovered them building War Machines. (TV: The War Machines) Dodo Chaplet became homeless shortly after leaving the First Doctor, but was rescued by James Stevens. (PROSE: Who Killed Kennedy)
In 1968, the Sentience possessed a homeless man named Billy Coote. (PROSE: Nightshade)
In 1969, Melody Pond became homeless after she escaped from the Silents. Six months later, in New York City, a tramp witnessed her regenerate. (TV: Day of the Moon)
In the 1970s, a tramp named Pigbin Josh was captured and killed by Axos. (TV: The Claws of Axos) Some years later, a tramp was run over by a hovercraft driven by the Third Doctor, who was chasing Lupton. (TV: Planet of the Spiders)
In 1992, a tramp nicknamed Leapy helped the Seventh Doctor defeat a Gantac invasion. (COMIC: Invaders from Gantac!) Later, another tramp became the Doctor's companion. (PROSE: The Tramp's Story)
In 1997, vampires killed many homeless people in San Francisco for their blood. (PROSE: Vampire Science)
On a Christmas Eve in the late 20th century, the Second Doctor, Jamie McCrimmon and Zoe Heriot stopped a desperate homeless man named Charlie from robbing the Midnight Mission in Los Angeles. (PROSE: Goodwill Toward Men)
In the early 21st century, with increasing pollution bringing declining health, the Butler Institute acquired homeless people as a source of replacement organs for the corporation's employees. (PROSE: Cat's Cradle: Warhead)
Circa 2006, Torchwood One abducted several homeless people and experimented on them with alien DNA, eventually creating the Chimera. (COMIC: The Legacy of Torchwood One!)
In 2007, a Bruydac killed several homeless people in Cardiff for their spinal fluid. (PROSE: Another Life)
In 2009, Eve abducted four homeless people for companionship. (TV: The Mad Woman in the Attic)
In late December of that year, the Saxon Master killed two homeless men, Tommo and Ginger, for their life force. (TV: The End of Time)
In 2011, a homeless man witnessed a Metalkind's arrival on Earth. He later told Sarah Jane Smith and Rani Chandra what he had seen. (TV: Sky)
Later that year, Clyde Langer met and befriended Ellie Faber and other homeless people when he was under Hetocumtek's curse. (TV: The Curse of Clyde Langer)
In 2012, Henry van Statten, who often had his employees mind-wiped and abandoned on the streets of various cities, suffered this fate himself at the hands of Diana Goddard as punishment for all the deaths caused by his Dalek. (TV: Dalek)
In 2050, Darius Pike encountered two tramps in a junkyard. They locked him in a wardrobe for invading their territory. (TV: Fear Itself)
On Pete's World, John Lumic had Cybus Industries round up homeless people and convert them into Cybermen. (TV: Rise of the Cybermen)
On an unnamed planet, a homeless man tried to eat a burger he found in a bin, only to find it was actually Avan Tarklu. (COMIC: The Shape Shifter)