We present evidence for the presence of a weak compact jet during a soft X-ray state of Cygnus X-1. Very-high-resolution radio observations were taken with the VLBA, EVN and MERLIN during a hard-to-soft spectral state change, showing the hard state jet to be suppressed by a factor of about 3–5 in radio flux and unresolved to direct imaging observations (i.e. ≲1 mas at 4 cm). High time-resolution X-ray observations with the RXTE-PCA were also taken during the radio monitoring period, showing the source to make the transition from the hard state to a softer state (via an intermediate state), although the source may never have reached the canonical soft state. Using astrometric very long baseline interferometry (VLBI) analysis and removing proper motion, parallax and orbital motion signatures, the residual positions show a scatter of ∼0.2 mas (at 4 cm) and ∼3 mas (at 13 cm) along the position angle of the known jet axis; these residuals suggest that there is a weak unresolved outflow, with varying size or opacity, during intermediate and soft X-ray states. Furthermore, no evidence was found for extended knots or shocks forming within the jet during the state transition, suggesting that the change in outflow rate may not be sufficiently high to produce superluminal knots.