We document a new phenomenon through which isolated, neutrally buoyant particles in density-stratified fluids are attracted to lateral walls, leading to an accumulation of matter in contact with the boundaries. Focusing on single bodies, we show that the mechanism for this attraction is a self-induced suction force which produces nearly constant accelerations of objects towards the nearest wall. We present an experimental, computational, and theoretical study to fully explore this new phenomenon. First, experiments exhibiting wall collapse will be presented documenting a region of near constant acceleration towards the wall. Next, flow structures are measured and compared quantitatively to computational simulations with spheres and cylinders, both in free space and near symmetry-disrupting vertical walls. Further computations reveal that the driving mechanism results from a competition between the pressure and viscous stress forces that enable what we term “lubrication screening”: the stratified system manages to overcome the well-known lubricating resistance when pushing a sphere towards a wall in a homogeneous fluid. By computationally comparing stratified and homogeneous cases with the same external towing forces, we establish the role of self-induced flows in decreasing this resistance. In particular, we present a reduced theoretical variable density Hele-Shaw model which explicitly predicts the development of a low-pressure region in the gap which provides suction toward the wall. Extensions to porous objects are discussed with theoretical and computational predictions showing how the wall-attracting force can be reversed, pushing the body away from the wall. Experiments with many bodies show that the strength, range, and speed of the wall attraction increase with aggregate size, yielding the ultimate accumulative trapping of particles on lateral boundaries. The ubiquity of stratification in nature suggests that these results could be relevant to many naturally occurring systems, such as marine aggregate accumulation near boundaries in moderately quiescent stratification.