Synthetic aperture radar (SAR) is an effective tool in detecting building damage. At present, more and more studies detect building damage using a single post-event fully polarimetric SAR (PolSAR) image, because it permits faster and more convenient damage detection work. However, the existence of non-buildings and obliquely-oriented buildings in disaster areas presents a challenge for obtaining accurate detection results using only post-event PolSAR data. To solve these problems, a new method is proposed in this work to detect completely collapsed buildings using a single post-event full polarization SAR image. The proposed method makes two improvements to building damage detection. First, it provides a more effective solution for non-building area removal in post-event PolSAR images. By selecting and combining three competitive polarization features, the proposed solution can remove most non-building areas effectively, including mountain vegetation and farmland areas, which are easily confused with collapsed buildings. Second, it significantly improves the classification performance of collapsed and standing buildings. A new polarization feature was created specifically for the classification of obliquely-oriented and collapsed buildings via development of the optimization of polarimetric contrast enhancement (OPCE) matching algorithm. Using this developed feature combined with texture features, the proposed method effectively distinguished collapsed and obliquely-oriented buildings, while simultaneously also identifying the affected collapsed buildings in error-prone areas. Experiments were implemented on three PolSAR datasets obtained in fully polarimetric mode: Radarsat-2 PolSAR data from the 2010 Yushu earthquake in China (resolution: 12 m, scale of the study area: ); ALOS PALSAR PolSAR data from the 2011 Tohoku tsunami in Japan (resolution: 23.14 m, scale of the study area: ); and ALOS-2 PolSAR data from the 2016 Kumamoto earthquake in Japan (resolution: 5.1 m, scale of the study area: ). Through the experiments, the proposed method was proven to obtain more than 90% accuracy for built-up area extraction in post-event PolSAR data. The achieved detection accuracies of building damage were 82.3%, 97.4%, and 78.5% in Yushu, Ishinomaki, and Mashiki town study sites, respectively.