In order to study the influence of the karst cave in the passive zone on the stability of the deep foundation pit of a subway station, relying on the deep foundation pit project of a subway station in Dalian, the expression of the minimum safe thickness of the karst cave side slab in the passive zone was established based on the elastic foundation beam theory and the cusp catastrophe theory. FLAC3D software was used to establish a numerical model to simulate the influence of different side slab thickness, length and buried depth of the passive zone on the stability of the foundation pit. Taking the simulation result of the maximum horizontal displacement of the pile as the concrete data, the sensitivity analysis of the factors affecting the stability of the foundation pit is carried out using the grey relational analysis method. The results are listed as follows. First of all, taking the thickness of the side slab of the karst cave as an indicator, the rationality of the expression of the minimum safe thickness of the side slab of the karst in the passive zone is verified by the numerical simulation results, and the influence of the thickness of the side slab of the karst cave on the stability of the foundation pit can be divided into a gentle zone, an obvious zone and a severe zone, and the caves in the severe zone must be reinforced. Secondly, as the length of the karst cave increases, the increase in the maximum horizontal displacement of the pile and the maximum settlement displacement of the ground will increase at an accelerated rate. Thirdly, when the buried depth of the karst cave is the same as the embedded depth of the pile, the maximum horizontal displacement of the pile and the maximum settlement displacement of the ground change drastically, and corresponding treatment measures should be taken. Fourthly, among the factors that affect the stability of foundation pits, the order of sensitivity from largest to smallest is the length of the cave, the thickness of the side plate of the cave, and the depth of the cave. It can be seen that it is necessary to study the influence of karst caves in the passive zone on the stability of foundation pits through theoretical analysis, numerical calculation, and statistical analysis before construction.