  Majorana bosons, that is, tight bosonic analogues of the Majorana fermionic
quasi-particles of condensed-matter physics, are forbidden for gapped free
bosonic matter within a standard Hamiltonian scenario. We show how the
interplay between dynamical metastability and non-trivial bulk topology makes
their emergence possible in non-interacting bosonic chains undergoing Markovian
dissipation. This leads to a distinctive form of topological metastability
whereby, consistent with the breakdown of Noether's theorem for open systems, a
conserved Majorana boson localized on one edge is paired with a distinct
symmetry generator localized on the opposite edge. We argue that Majorana
bosons are robust against disorder and identifiable by signatures in the
zero-frequency steady-state power spectrum. Our results suggest that
symmetry-protected topological phases for free bosons may arise in transient
metastable regimes, which are still stable over practical time scales.
