  We present an exact representation for decaying ZZ-branes within the dual
matrix model formulation of c=1 string theory. It is shown how to trade the
insertion of decaying ZZ-branes for a shift of the closed string background.
Our formlaism allows us to demonstrate that the conjectured world-sheet
mechanism behind the open-closed dualities (summing over disc insertions) is
realized here in a clear way. On the way we need to clarify certain infrared
issues - insertion of ZZ-branes creates solitonic superselection sectors.
