We investigate the correspondence between existence/stability of BPS states
in type II string theory compactified on a Calabi-Yau manifold and BPS
solutions of four dimensional N=2 supergravity. Some paradoxes emerge, and we
propose a resolution by considering composite configurations. This in turn
gives a smooth effective field theory description of decay at marginal
stability. We also discuss the connection with 3-pronged strings, the Joyce
transition of special Lagrangian submanifolds, and Pi-stability.Comment: 40 pages, 13 figures, reference adde