The possible consequences of a collision between a red giant and a relatively compact star (a main-sequence star or a white dwarf) are presented, and their astrophysical significance is discussed. The core-envelope structure of a red giant star leads, for a partial range of the initial encounter conditions, to the separation of these two components. Using a two-dimensional code, the hydrodynamics initiated in the envelope during and after such an event have been traced. Part of the envelope, in these cases, is dragged by the escaping core, while the rest of it disperses into space with typical velocities of 30 km/s. This might be the mechanism for the creation of gas clouds seen in the central part of galaxies, as was suggested by Lacy and coworkers (1982). 9 references.