Searches for neutrino-less double-beta decay ($0 u2beta$) place an important constraint on models where light fields beyond the Standard Model participate in the neutrino mass mechanism. While $0 u2beta$ experimental collaborations often consider various massless majoron models, including various forms of majoron couplings and multi-majoron final-state processes, none of these searches considered the scenario where the majoron $phi$ is not massless, $m_phisim$~MeV, of the same order as the $Q$-value of the $0 u2beta$ reaction. We consider this parameter region and estimate $0 u2betaphi$ constraints for $m_phi$ of order MeV. The constraints are affected not only by kinematical phase space suppression but also by a change in the signal to background ratio characterizing the search. As a result, $0 u2betaphi$ constraints for $m_phi>0$ diminish significantly below the reaction threshold. This has phenomenological implications, which we illustrate focusing on high-energy neutrino telescopes. Our results motivate a dedicated analysis by $0 u2beta$ collaborations, analogous to the dedicated analyses targeting massless majoron models.
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