High-energy electrons that are used as a probe of specimens in transmission electron microscopy exhibit a complex and rich behavior due to multiple scattering. Among other things, understanding the dynamical effects is needed for a quantitative analysis of atomic-resolution images and spectroscopic data. In this study, state-correlation functions are computed within the multislice approach that allow to elucidate behaviors of transversely bound states in crystals. These states play an important role as a large fraction of current density can be coupled into them via focused electron probes. We show that bound states are generically unstable and decay monoexponentially with crystal depth. Their attenuation is accompanied by a resonant intensity transfer to Bessel-like wavefunctions that appear as Laue rings in the far-field diffraction patterns. Behaviors of bound states are also quantified when thermal effects are included, as well as point defects. This approach helps to bridge the Bloch wave and multisliced electron propagation pictures of dynamical scattering providing new insights into fundamental solutions of the wave equation, and may assist in developing quantitative STEM/TEM imaging techniques.