  Majorana bound states are interesting candidates for applications in
topological quantum computation. Low energy models allowing to grasp their
properties are hence conceptually important. The usual scenario in these models
is that two relevant gapped phases, separated by a gapless point, exist. In one
of the phases, topological boundary states are absent, while the other one
supports Majorana bound states. We show that a customary model violates this
paradigm. The phase that should not host Majorana fermions supports a
fractional soliton exponentially localized at only one end. By varying the
parameters of the model, we describe analytically the transition between the
fractional soliton and two Majorana fermions. Moreover, we provide a possible
physical implementation of the model. We further characterize the symmetry of
the superconducting pairing, showing that the odd-frequency component is
intimately related to the spatial profile of the Majorana wavefunctions.
