  Wide, fragile binary stellar systems are found in the galactic field, and
have recently been noted in the outskirts of expanding star clusters in
numerical simulations. Energetically soft, with semi-major axes exceeding the
initial size of their birth cluster, it is puzzling how these binaries are
created and preserved. We provide an interpretation of the formation of these
binaries that explains the total number formed and their distribution of
energies. A population of weakly bound binaries can always be found in the
cluster, in accordance with statistical detailed balance, limited at the soft
end only by the current size of the cluster and whatever observational criteria
are imposed. At any given time, the observed soft binary distribution is
predominantly a snapshot of a transient population. However, there is a
constantly growing population of long-lived soft binaries that are removed from
the detailed balance cycle due to the changing density and velocity dispersion
of an expanding cluster. The total number of wide binaries that form, and their
energy distribution, are insensitive to the cluster population; the number is
approximately one per cluster. This suggests that a population composed of many
dissolved small-N clusters will more efficiently populate the field with wide
binaries than that composed of dissolved large-N clusters. Locally such
binaries are present at approximately the 2% level; thus the production rate is
consistent with the field being populated by clusters with a median of a few
hundred stars rather than a few thousand.
