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 semimajor 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 1 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 per cent 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.