  The $d = 2$ string admits a black hole solution and also a singular solution
when tachyon back reaction is included. It is of importance to know if the
former solution can evolve into a later one. An explicit solution describing
this process is difficult to obtain. We present here a scenario in which such
an evolution is very likely to occur. In essence, it takes place when a
derivative discontinuity is seeded in the dilaton field by an incident tachyon
pulse. An application of this scenario to $1 + 1$ dimensional toy models
suggests that a black hole can evolve into a massive remnant, strengthening its
candidacy for the end state of a black hole.
