Evolution of D-branes Under Closed String Tachyon Condensation

We study the evolution of stable D-branes of C/Z_n and twisted circle theories in the process of closed string tachyon condensation. We interpret the fractional branes in these backgrounds as type II branes wrapping (`blown up') cycles, and trace the evolution of the corresponding cycles under tachyon condensation. We also study RG flows of the corresponding N=2 boundary conformal field theories. We find flows along which fractional D-branes either disappear or evolve into other fractional D-branes, and other flows along which bulk branes either disappear or evolve into stable branes.