A Failed incarnation is someone who was the intended Nerevarine (not to be confused with the actual Nerevarine), the reincarnation of Indoril Nerevar, as dictated by the Nerevarine Prophecy of Azura. All of these people were thought to be "possessed" by the spirit of the warlord, but they had critical flaws that made them destined to fail the fulfilment of the prophecy, and as such were revealed to be false Nerevarines.
The first known intended Nerevarine was Ane Teria, who was a holy crusader of the Tribunal Temple during the Tribunal's golden age in the early First Era, some time after the Battle of Red Mountain in 1E 700. She wrote writings, later known as Apographa, that were suppressed by the Tribunal Temple. She followed the false gods unquestionably, and only began to believe the Nerevarine Prophecy when it was too late.
During the Akaviri Invasions of 1E 2703, an incarnate named Conoon Chodala, who was the ashkhan of his Ashlander tribe, led his people against the eastern invaders as the Imperials fled. He followed the Akaviri all the way into the strongholds and Red Mountain, killing them in their own blood. He did not listen to the Mabrigash, instead craving glory, though did not see his real enemies of the Tribunal and House Dagoth.
Erur-Dan, another incarnate, saw Morrowind make a treaty with either the Reman Empire during the Four Score War, or the Septim Empire during the Tiber Wars. Humiliated by the surrender, he swore vengeance against the Empire and Tribunal alike. In later years, he despaired, and died fighting the Blight creatures at Red Mountain.
In the late years of the Tribunate, Idrenie Nerothan was an incarnate who demoralized and repelled the Akaviri invaders in 2E 572. She knew nothing of Dagoth Ur and the Nerevarine Prophecy until she took refuge with the Ashlanders. She died trying to loot Kogoruhn, a Sixth House stronghold in the northern Ashlands, considering her actions foolish.
In the waning years of the Second Era, Hort Ledd was the intended incarnate. He was a thinker and not a doer, and though chosen by the prophecy, he was not a hero and did not fulfill the prophecy. He died around 3E 27, in the last days of turmoil and unrest under the Septim Empire's rule over Morrowind.
Peakstar was an incarnate who survived the Blight, but fell in battle with an Ash Vampire. She did not master the arts of war, and did not learn the ways of the Great Houses, so she could not be named Hortator. In 3E 427, her spirit guided the true Nerevarine, helping them fulfill the prophecy.