A control strategy integrating braking force redistribution and path tracking was proposed to address the problem that instability and yawing were prone to occur when vehicles equipped with electromechanical brake (EMB) system experience braking failures during cornering. Gaussian perturbation and staged optimization were introduced to improve the algorithm in order to mitigate the deficiencies of the slime mould algorithm (SMA). The enhanced SMA was employed to optimize the weight matrix of the linear quadratic regulator (LQR). The improved LQR algorithm was utilized to compute the vehicle’s yaw moment upon detection of a single-wheel failure in the EMB system, followed by braking force redistribution to maintain vehicle stability. The pure pursuit algorithm was modified by shifting the tracking control point to enhance the response speed of the algorithm. An adaptive fuzzy control algorithm was incorporated to accommodate dynamic factors such as road conditions and vehicle speed, thus improving its adaptability. Path tracking was implemented to guide the vehicle along a predefined trajectory until a safe stop when a double-wheel failure was detected in the EMB system. The experimental results demonstrated that the maximum lateral deviation was reduced by 59.15% for single-wheel failure and by 41.95% for double-wheel failure compared with conventional methods. The proposed control strategy can more effectively ensure driving safety during cornering braking failure.