Stability and stabilization issues of two-dimensional linear time-invariant switched systems with unstable subsystems and multi-equilibria are investigated. Firstly, for the case that each subsystem has a unique focus or center and these equilibria are different from each other, a unique determined region containing all equilibria is defined, and a concept of region stability is given. Then, based on the region stability introduced, several simple criteria of global region asymptotical stability are proposed for such switched systems via the mathematical analysis method. Global asymptotical region stabilizing controls and corresponding algorithms are also designed for the systems. Finally, an illustrative example and its simulations demonstrate the effectiveness and practicality of the obtained stability and stabilization results.