Good plasma performance in magnetic fusion devices of different types, both tokamaks and helical devices, is achieved normally if the plasma density does not exceed a certain limit. In devices with a divertor, such as tokamaks JET, JT-60U, and heliotron large helical device (LHD), by approaching the density limit, the plasma detaches from the divertor target plates so that the particle and heat fluxes onto the targets reduce dramatically. This is an attractive scenario for fusion reactors, offering a solution to the plasma-wall interaction problem. However, the main concerns by realizing such a scenario are the stability of the detached zone. The activity on the heliotron LHD aimed on detachment stabilization, by applying a resonant magnetic perturbation (RMP) and generating a wide magnetic island at the plasma edge, will be reviewed. Also, theoretical models, explaining the detachment conditions, low-frequency oscillations at the detachment onset, and mechanisms of the detached plasma stabilization by RMP, will be discussed.