This work investigates the long-term evolution of dilute solute atoms in face-centered-cubic (fcc) alloys driven by sustained vacancy fluxes, as for instance in the case of materials subjected to energetic particle irradiation. Employing the five jump frequency framework, we provide compact analytic expressions of the Onsager matrix for dilute vacancy-solute systems in form of a ratio of polynomial functions of jump frequencies. The drag ratio is found to be a function of only two independent variables, which enables a systematic study of both the flux coupling and trapping behavior between solutes and point defects. Using an existing diffusivity database for a total of 182 solutes in 5 fcc solvents, we show that, while most vacancy-binding solutes have indeed a positive drag ratio, there are some solutes with positive, but small, or even negative drag ratio. This previously unnoticed feature is interesting as it would ensure that the trapping solute remains in the matrix despite the accumulation of irradiation dose. In the case where the drag ratio is positive, we propose a kinetic model of solute depletion over time due to flux coupling with vacancies and apply it to a Cu-1 at. % Sb alloy. This study reveals that solutes are not simply dragged to sinks by point defects, but affect the flux of point defects to sinks by modifying the transport coefficients and the driving force for point-defect elimination.