  We demonstrate that the one-dimensional helical Majorana edges of
two-dimensional time-reversal symmetric topological superconductors (class
DIII) can become gapless and insulating by a combination of random edge
velocity and interaction. Such a gapless insulating edge breaks time-reversal
symmetry inhomogeneously, and the local symmetry broken regions can be regarded
as static mass potentials or dynamical Ising spins. In both limits, we find
that such glassy Majorana edges are generically exponentially localized and
trap Majorana zero modes. Interestingly, for a statistically time-reversal
symmetric edge, the low-energy theory can be mapped to a Dyson model at zero
energy, manifesting a diverging density of states and exhibiting marginal
localization (i.e., a diverging localization length). Although the ballistic
edge state transport is absent, the localized Majorana zero modes reflect the
nontrivial topology in the bulk. Experimental signatures are also discussed.
