We discuss two variants of supersymmetric theories that allow to bypass or weaken greatly the limits on the minimal supersymmetric model obtained during the LHC RUN 1 and RUN 2 and to explain why we don't observe light superpartners with masses below the TeV threshold. This situation is uncomfortable in some sense because it definitely contradicts the naturalness requirements of the MSSM. Stealth and R-parity violating SUSY models look promising in this context. It seems that such approaches can help us solve the problem. Possible experimental signatures including prompt superpartner decay chains and events with long-lived particles are considered, and the first results of the ATLAS and CMS collaborations on related topic are discussed.