The second peak in the Fe xvi 33.5 nm line irradiance observed during solar flares by the Extreme-Ultraviolet Variability Experiment (EVE) is known as the EUV late phase. Our previous paper in 2013 by Liu et al. found that the main emissions in the late phase are originated from large-scale loop arcades that are closely connected to but different from the post-flare loops (PFLs), and we also proposed that a long cooling process without additional heating could explain the late phase. In this paper, we define the extremely large late phase because it not only has a bigger peak in the warm 33.5 irradiance profile, but also releases more EUV radiative energy than the main phase. Through detailed inspection of the EUV images from three points of view, it was discovered that aside from the later-phase loop arcades, the main contributor of the extremely large late phase is a hot structure that fails to erupt. This hot structure is identified as a flux rope, which is quickly energized by the flare reconnection and later on continuously produces the thermal energy during the gradual phase. Together with the late-phase loop arcades, the flux rope failing to erupt with the additional heating create the extremely large EUV late phase.