[en] Many giant exoplanets are found near their Roche limit and in mildly eccentric orbits. In this study, we examine the fate of such planets through Roche-lobe overflow as a function of the physical properties of the binary components, including the eccentricity and the asynchronicity of the rotating planet. We use a direct three-body integrator to compute the trajectories of the lost mass in the ballistic limit and investigate the possible outcomes. We find three different outcomes for the mass transferred through the Lagrangian point L ₁: (1) self-accretion by the planet, (2) direct impact on the stellar surface, and (3) disk formation around the star. We explore the parameter space of the three different regimes and find that at low eccentricities, $e\lesssim <!--\; ???\; -->0.2$, mass overflow leads to disk formation for most systems, while, for higher eccentricities or retrograde orbits, self-accretion is the only possible outcome. We conclude that the assumption often made in previous work that when a planet overflows its Roche lobe it is quickly disrupted and accreted by the star is not always valid.