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Abstract We propose to search for the open heavy-flavor exotic states with the quark components of $$Qs{\bar{u}}{\bar{d}}$$ Q s u ¯ d ¯ with $$Q=b,c$$ Q = b , c via their weak decays. If there exist such exotic states below the BK or DK thresholds, they can only decay weakly. The advantages include: (i) the experimental backgrounds from the secondary decay vertex are much lower due to the long lifetimes, (ii) the productions are large enough for only one heavy quark in such states, (iii) the thresholds of BK or DK are about 260 MeV higher compared to the $$B_s\pi $$ B s π or $$D_s\pi $$ D s π thresholds of the configurations of $$Qu{\bar{s}}{\bar{d}}$$ Q u s ¯ d ¯ or $$Qd{\bar{s}}{\bar{u}}$$ Q d s ¯ u ¯ , with a higher possibility to exist such weakly-decay particles, and (iv) if observed, their inner structures are easier understood since they can not be induced by the kinematic effects.