Influenza A virus (IAV) spreads through airborne particles ranging from sub-micrometer to millimeter-sized droplets. The stability of airborne IAV remains difficult to estimate and depends, among others, on the respiratory matrix composition and the size-dependent drying kinetics. Here, we combine experiments on deposited millimeter-sized saline droplets with a biophysical aerosol model to quantify the effect of NaCl on IAV stability, in the presence and absence of sucrose as organic co-solute. We demonstrate that IAV inactivation in dilute saline droplets after exposure to air at various relative humidities is driven by the increasing NaCl molality during water evaporation, rather than by efflorescence, i.e. the precipitation of salt crystals. For pure aqueous NaCl droplets, we find the inactivation rate constant to depend exponentially on NaCl molality, which enables us to simulate inactivation under both efflorescing and deliquescing conditions. We provide evidence for virion integrity loss as the primary inactivation mechanism. Addition of sucrose attenuates IAV inactivation, which we attribute to two mechanisms: first, sucrose decreases the NaCl molality during the drying phase, and second, at equal NaCl molality, sucrose shields IAV from the inactivating effects of NaCl. These experiments help advance our understanding of IAV stability in expiratory particles and the associated transmission risks.