  We identify reactions which destroy 7Be and 7Li during big bang
nucleosynthesis (BBN) in the scenario of BBN catalyzed by a long-lived
sub-strongly interacting massive particle (sub-SIMP or X particle). The
destruction associated with non radiative X captures of the nuclei can be
realized only if the interaction strength between an X particle and a nucleon
is properly weaker than that between two nucleons to a degree depending on the
mass of X. Binding energies of nuclei to an X particle are estimated taking the
mass and the interaction strength to nuclei of the X as input parameters.
Nuclear reaction rates associated with the X are estimated naively, and adopted
in calculating evolutions of nuclear abundances. We suggest that the 7Li
problem, which might be associated with as-yet-unrecognized particle processes
operating during BBN, can be solved if the X particle interacts with nuclei
strongly enough to drive 7Be destruction but not strongly enough to form a
bound state with 4He of relative angular momentum L=1. Justifications of this
scenario by rigorous calculations of reaction rates using quantum mechanical
many-body models are highly desirable since this result involves many
significant uncertainties.
