  The traditional black hole has a horizon, with a singularity inside the
horizon. But actual microstates of black holes are `fuzzballs', with no horizon
and a complex internal structure. We take the simplest hole in string theory --
the extremal 2-charge D1D5 hole -- and study a simple effect that is a
consequence of this internal structure of the fuzzball. Suppose we have a NS1
string wrapping the compact circle of the fuzzball solution. In the traditional
black hole solution this circle is directly tensored with the remaining
directions, and does not shrink to zero size. Thus a part of the string can
fall behind the horizon, but not `unwind'. In the fuzzball geometry, this
circle makes a nontrivial geometric structure -- the KK monople -- by mixing
with the other directions, and thus shrinks to zero at the core of the
monopole. Thus the string can `unwind' in the fuzzball geometry, and the
winding charge is then manifested by a nontrivial field strength living on the
microstate solution. We compute this field strength for a generic microstate,
and comment briefly on the physics suggested by the unwinding process.
