If massive neutrinos are the Majorana particles and have a normal mass ordering, the effective mass term $〈 m〉^{}_{ee}$ of a neutrinoless double-beta ($0ν 2β$) decay may suffer significant cancellations among its three components and thus sink into a decline, resulting in a "well" in the three-dimensional graph of $|〈 m〉^{}_{ee}|$ against the smallest neutrino mass $m^{}_1$ and the relevant Majorana phase $ρ$. We present a new and complete analytical understanding of the fine issues inside such a well, and discover a novel threshold of $|〈 m〉^{}_{ee}|$ in terms of the neutrino masses and flavor mixing angles: $|〈 m〉^{}_{ee}|^{}_* = m^{}_3 \sin^2\theta^{}_{13}$ in connection with $\tan\theta^{}_{12} = \sqrt{m^{}_1/m^{}_2}$ and $ρ =π$. This threshold point, which links the {\it local} minimum and maximum of $|〈 m〉^{}_{ee}|$, can be used to signify observability or sensitivity of the future $0ν 2β$-decay experiments. Given current neutrino oscillation data, the possibility of $|〈 m〉^{}_{ee}|