Recent theoretical works have shown that matter swapping between two parallel braneworlds could occur under the influence of magnetic vector potentials. In our visible world, galactic magnetism possibly produces a huge magnetic potential. As a consequence, this Letter discusses the possibility to observe neutron disappearance into another braneworld in certain circumstances. The setup under consideration involves stored ultracold neutrons - in a vessel - which should exhibit a non-zero probability p to disappear into an invisible brane at each wall collision. An upper limit of p is assessed based on available experimental results. This value is then used to constrain the parameters of the theoretical model. Possible improvements of the experiments are discussed, including enhanced stimulated swapping by artificial means.