It disappears from the fossil record, or historic reports of its existence cease;
The reduced population no longer plays a significant role in ecosystem function; or
The population is no longer viable. There are no individuals able to reproduce, or the small population of breeding individuals will not be able to sustain itself due to inbreeding depression and genetic drift, which leads to a loss of fitness.
In plant populations, self-incompatibility mechanisms may cause related plant specimens to be incompatible, which may lead to functional extinction if an entire population becomes self-incompatible. This does not occur in larger populations.
In polygynous populations, where only a few males leave offspring, there is a much smaller reproducing population than if all viable males were considered. Furthermore, the successful males act as a genetic bottleneck, leading to more rapid genetic drift or inbreeding problems in small populations.
On May 10, 2019, the Australian Koala Foundation issued a press release that opened with the sentence "The Australian Koala Foundation (AKF) believes Koalas may be functionally extinct in the entire landscape of Australia." The press release was reported on by multiple news agencies around the world, with most repeating the AKF's statement. Despite this, Koalas are not currently considered functionally extinct; while their population has decreased, the IUCN Red List lists them only as "Vulnerable". The AKF's press release was released on the eve of the 2019 elections in Australia, where topics such as climate change were major issues, and may have been a political ploy intended to bring attention to man-made threats such as habitat destruction and global warming.
Distinct animal populations can also become functionally extinct. In 2011, a 3-year survey of the wildlife population in the Bénoué Ecosystem of North Cameroon (the Bénoué, Bouba-Ndjidda, and Faro national parks, and 28 hunting zones surrounding the parks), concluded that the North Cameroon population of cheetahs (Acinonyx jubatus) and African wild dogs (Lycaon pictus) were now functionally extinct. Non-Northern Cameroonian cheetahs are listed as "Vulnerable" by the IUCN Red List. 
^Yoshida, Kate Shaw (2013-07-12). "Not yet gone, but effectively extinct". arstechnica. Retrieved 2019-05-19. But there is another type, called “functional extinction,” which takes a more ecological approach. Some scientists argue that the threshold for extinction should not be the complete disappearance of a species, but instead the point at which there aren’t enough individuals left in that species to perform whatever roles it was playing in the ecosystem.
^Pérez-González, J; Mateos, C; Carranza, J (2009-04-01). "Polygyny can increase rather than decrease genetic diversity contributed by males relative to females: evidence from red deer". Molecular Ecology. 18 (8): 1591–1600. doi:10.1111/j.1365-294X.2009.04150.x. PMID19302345.
^Caryl-Sue, National Geographic Society, ed. (2013-12-17). "Dec 12, 2006 CE: Chinese River Dolphin Declared Extinct". NationalGeographic.org. Mary Crooks, National Geographic Society. Retrieved 2019-05-18. On December 12, 2006, biologists declared the baiji (Chinese river dolphin) "functionally extinct." [...] [T]here have been no confirmed baiji sightings in recent years.
^"Yangtze Finless Porpoise". World Wildlife Fund. Retrieved 2019-05-18. The Yangtze River, the longest river in Asia, used to be one of the only two rivers in the world that was home to two different species of dolphin—the Yangtze finless porpoise and the Baiji dolphin. However, in 2006 the Baiji dolphin was declared functionally extinct. This was the first time in history that an entire species of dolphin had been wiped off the planet because of human activity.
^Phillips, Tom (2016-10-10). "China's 'extinct' dolphin may have returned to Yangtze river, say conservationists". Beijing, China: The Guardian. Retrieved 2019-05-18. Chinese conservationists believe they may have caught a rare glimpse of a freshwater dolphin that was declared functionally extinct a decade ago having graced the Yangtze river for 20 million years. Scientists and environmentalists had appeared to abandon hope [...] after they failed to find a single animal during a fruitless six-week hunt along the 6,300-km (3,915-mile) waterway in 2006. [...] [T]he unconfirmed sighting occurred during a seven-day search mission down the Yangtze that began in the city of Anqing on 30 September .
^Xiang, Luan (2018-05-08). ZD (ed.). "Feature: Hope prevails for the baiji dolphin's comeback". Beijing, China: XiahuaNet. Retrieved 2019-05-18. Earlier this week, the China Biodiversity Conservation and Green Development Foundation (CBCGDF) released a photograph of a baiji lookalike, captured last month in a section of the Yangtze near Wuhu in the eastern province of Anhu. [...] The institute said it would be imprudent to identify the animal in a photograph without further evidence. Nonetheless, it is too soon to label the species "extinct."
^Schulz, Martin (2004). National Recovery Plan for the Christmas Island Shrew (Crocidura attenuata trichura). Australian Government, The Department of the Environment and Energy. ISBN0-642-55011-5. The Christmas Island Shrew was thought to be extinct until the accidental separate finding of two individuals in 1985... Information indicating the unconfirmed capture of two other shrews in 1958 when South Point (approx.: 10°33'S, 105°39'E) was being cleared for mining was provided by D. Powell (pers. comm. 1997 cited in Meek 1998).
^Platt, John R. (2014-12-23). "Holiday Species Snapshot: Christmas Island Shrew". Scientific American. Retrieved 2019-05-18. There's an official species recovery plan in place, though, just in case the shrews ever show up again. Sadly, that seems like it would require a Christmas miracle.
^Platt, John R. (2016-01-26). "The Yangtze Giant Softshell Turtle Just Got 25 Percent Closer to Extinction". Scientific American. Retrieved 2019-05-18. The massive turtle known as Cu Rua... passed away last week. [...] Cu Rua was one of the last four Yangtze giant softshell turtles (Rafetus swinhoei) left in the world. Now only three remain: a turtle of unknown gender in another lake outside of Hanoi and a male-female pair in China.
^Gibbens, Sarah (2017-05-23). "There Are Only 3 of These Turtles Left on Earth". Retrieved 2019-05-18. In the waters of the Yunnan Province of China, a team of conservationists is hoping to find a turtle with some very valuable sperm. [...] A male and female are in captivity in the Suzhou Zoo in China, and one wild turtle lives in a Vietnamese lake called Dong Mo. [...] In February of , a fourth turtle... died in captivity in Vietnam, reducing the world population by a quarter.
^Wang, Serenitie (2019-04-15). "One of world's most endangered turtles dies, leaving 3 left". Beijing, China. Retrieved 2019-05-18. The last known female Yangtze giant softshell turtle has died in China, according to Chinese state media, potentially dooming the species to extinction. [...] Now, there are only three left in the world, according to the Suzhou Daily.
^Smith, Nicola (2019-04-15). "Turtle species on brink of extinction as last-known female dies in China". Retrieved 2019-05-18. One of the world’s rarest turtles, a Yangtze giant softshell, has died in a Chinese zoo, leaving only three of the critically endangered species left. The turtle was the last confirmed female in the world when she died during fertility treatment, raising the grim prospect that the species, which is also known as the Red River giant and is native to China and Vietnam, may now be functionally extinct.
^"South China Tiger". World Wildlife Fund. Retrieved 2019-05-18. The South China tiger population was estimated to number 4,000 individuals in the early 1950s. [...] By 1996 the population was estimated to be just 30-80 individuals. Today the South China tiger is considered by scientists to be “functionally extinct,” as it has not been sighted in the wild for more than 25 years.
^AFP (2016-04-06). "Tigers declared extinct in Cambodia". The Guardian. Retrieved 2019-05-18. The last tiger was seen on camera trap in the eastern Mondulkiri province in 2007, [the World Wildlife Fund] said. “Today, there are no longer any breeding populations of tigers left in Cambodia, and they are therefore considered functionally extinct,” the conservation group said in a statement.