Since their formation, asteroids since their formation have experienced little physical, geological or thermal evolution. Like comets they are thought to be among the most pristine remnants of the early solar system. One physical process, however, has played a major role since the ancient times: collisions. Dynamical families were produced by catastrophic collisions involving large enough energy to break the parent body. Other lines of evidence suggest that catastrophic collisions can also produce rubble-piles, i.e., loosely bound of post-collisional aggregates that re-accumulate to form a single body, and are kept together by gravity. The main objective of this work is to understand if---and under what conditions---Jacobi ellipsoids or other equilibrium figures can be obtained naturally by this way. This is done by performing numerical experiments simulating the re-accumulation process, and by performing high-angular resolution observations in order to better constrain the shape and density of the targets. It is shown that the outcomes of reaccumulation events tend to produce a rather narrow variety of possible shapes, and in some cases also binary systems.