  We discuss renormalization group flows in two-dimensional quantum field
theories with (0,2) supersymmetry. We focus on theories with UV described by a
Landau-Ginzburg Lagrangian and use the chiral algebra to constrain the IR
dynamics. We present examples where the structure of the chiral algebra is
incompatible with unitarity of the IR superconformal theory and discuss the
implications of this result for programs of classifying (0,2) SCFTs as
endpoints of flows from simple Lagrangian theories.
