<p>The study explores the finite-time stabilization of switched stochastic planar systems that face asymmetric time-varying output constraints. A key innovation in this research is the elimination of the local Lipschitz condition for switched stochastic nonlinear systems, prompting the development of new criteria for the existence of a global weak solution and stochastic finite-time stability. To tackle the challenges posed by asymmetric time-varying output constraints, we introduce a novel state-constrained transformation, which serves as an alternative to the traditional use of barrier Lyapunov functions. This transformation ensures that output constraints are not violated if the states of the transformed system remain almost surely bounded. We design radially unbounded Lyapunov functions for further investigation, which confirm the existence of a solution and finite-time stability for non-Lipschitzian stochastic systems. Finally, the effectiveness of the proposed continuous output-feedback control strategy is confirmed through simulation examples.</p>