We explore with collisional gravitational N-body models the evolution of binary stars in initially fragmented and globally subvirial clusters of stars. Binaries are inserted in the (initially) clumpy configurations so as to match the observed distributions of the field-binary-stars' semimajor axes a and binary fraction versus primary mass. The dissolution rate of wide binaries is very high at the start of the simulations, and is much reduced once the clumps are eroded by the global infall. The transition between the two regimes is sharper as the number of stars N is increased, from N = 1.5 k up to 80 k. The fraction of dissolved binary stars increases only mildly with N, from ≈15 per cent to ≈25 per cent for the same range in N. We repeated the calculation for two initial system mean number densities of 6 per pc 3 (low) and 400 per pc 3 (high). We found that the longer free-fall time of the low-density runs allows for prolonged binary-binary interactions inside clumps and the formation of very tight (a ≈ 0.01 au) binaries by exchange collisions. This is an indication that the statistics of such compact binaries bear a direct link to their environment at birth. We also explore the formation of wide (a 5 × 10 4 au) binaries and find a low (≈0.01 per cent) fraction mildly bound to the central star cluster. The high-precision astrometric mission Gaia could identify them as outflowing shells or streams.