The large-scale mining of underground mineral resources will lead to the formation of mined-out areas, which will lead to a series of geological and environmental problems. By selecting the Mudengdong village as a case study, this paper uses geodetic satellite remote sensing technologies to perform qualitative analyses and summarize the geological engineering conditions of the factory. Afterwards, the predominant factors that affect the stability of foundation are determined based on the geological survey of karst in goaf structures. Finally, the finite element software ANSYS is used to comprehensively study the karst problem. The results indicate that (1) the karst development pattern in the study area is controlled by the Beiyin mountain fault, in which case the karst in the basin, in the foot slope, or in the pass section is more widespread than in the slope section. Moreover, the karst generally has a vertical form and is in the early karst stage of development; (2) surface rainwater infiltration, earthquakes, and load pressure are the three major factors that affect karst collapse in the study area; (3) by simulating the development of karst caves and the bearing capacity of the karst roof in the goaf structure under different conditions, it is recommended that only civil buildings with not more than three floors can be built in the village. Overburdened soil thicknesses between 6 and 10 m and civil buildings with heights less than 6 m are not suitable parameters for construction activities. If there are hidden soil holes under the overburden layer, dynamic consolidation needs to be applied in order to destroy the structure of the soil layer and to ensure the safety of personnel.