A resonant state at $3.21^{+0.12}_{-0.04}$,MeV, located just above the one-neutron separation threshold, was observed for the first time in $^{12}$Be from the $^{11}$Be,$(d,p)^{12}$Be one-neutron transfer reaction in inverse kinematics. This state is assigned a spin-parity of $0^-$, according to the distorted-wave Born approximation (DWBA) and decay-width analysis. Gamow coupled-channel (GCC) and Gamow shell-model (GSM) calculations show the importance of the continuum-coupling, which dramatically influences the excitation energy and ordering of low-lying states. Various exotic structures associated with cross-shell intruding configurations in $^{12}$Be and in its isotonic nucleus $^{11}$Li are comparably discussed.
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