We examine the remnant phase of radio galaxies using three-dimensional hydrodynamical simulations of relativistic jets propagating through cluster environments. By switching the jets off once the lobes have reached a certain length we can study how the energy distribution between the lobes and shocked intra-cluster medium compares to that of an active source, as well as calculate synchrotron emission properties of the remnant sources. We see that as a result of disturbed cluster gas beginning to settle back into the initial cluster potential, streams of dense gas are pushed along the jet axis behind the remnant lobes, causing them to rise out of the cluster faster than they would due to buoyancy. This leads to increased adiabatic losses and a rapid dimming. The rapid decay of total flux density and surface brightness may explain the small number of remnant sources found in samples with a high flux density limit and may cause analytic models to overestimate the remnant fraction expected in sensitive surveys such as those now being carried out with LOFAR.