A study is made of the boundary regions of magnetic structures formed either near the last closed flux surface of the main magnetic configuration in a stellarator or near magnetic islands in more general toroidal confinement systems with topologically equivalent sheared magnetic configurations. With a relatively simple approximate analytic model based on the perturbation method, it was possible not only to reproduce earlier results on the destruction of hyperbolic magnetic axes in the three-dimensional toroidal magnetic configurations under consideration but also to obtain some new results, in particular, to analytically estimate the sizes of the separatrix regions of stochastic magnetic fields that arise in the main stellarator configuration and also near the inner chains of magnetic islands in any magnetic configuration under consideration. It is notable that the boundary region of the main stellarator magnetic configuration is a multiply connected structure, the outer part of which is largely governed by the current distribution in the magnetic system creating this configuration.