Humanity is on its last lap. A once great empire has been reduced to a single Dyson sphere around the dying sun, and most of the matter of the solar system has already been incorporated into this last bastion of survival. Any activity which leaks energy out of the sphere is suspect, and only very rarely do humans venture outside anymore, on occasional expeditions to salvage stray asteroids or other rubble.
In this scenario, the only way space travel could be considered acceptable at all is if it can be performed at an extremely low energy cost, so that the energy gain of towing in an old shuttle or piece of rock surpasses the expenditure of making the trip in the first place.
My thought is that a type of travel that could be conceivable in this world would be using laser sails to travel outwards, and then falling back towards the home sphere through natural gravity. Heat inefficiencies from the lasers themselves could be absorbed back into the sphere, and the kinetic energy of the ships could be reclaimed on return.
Is this feasible? The ships can be assumed to be almost fully contained and self-sufficient and able to sustain a small crew for months or years. Some energy/heat leakage will be unavoidable, but is it possible that you can still go energy-positive through such a scheme, or is it just utterly ridiculous? Speed and comfort can be sacrificed, since we're talking about squeezing just a few more years of sustainable living from a solar system which is already at the limit.
If not reasonable based on what I laid out here, are there other options which could work better?