Recent experiments have introduced a new concept for analyzing the photoemission spectra of correlated electrons -- the remnant Fermi surface (rFs), which can be measured even in systems which lack a conventional Fermi surface. Here, we analyze the rFs in a number of interacting electron models, and find that the results fall into two classes. For systems with pairing instabilities, the rFs is an accurate replica of the true Fermi surface. In the presence of nesting instabilities, the rFs is a map of the resulting superlattice Brillouin zone. The results suggest that the gap in Ca_2CuO_2Cl_2 is of nesting origin.

4 pages LaTex, 3 ps figures