  Condensed matter systems are continuously subjected to dissipation, which
often has adverse effects on quantum phenomena. We focus on the impact of
dissipation on a superconducting Rashba nanowire. We reveal that the system can
still host Majorana zero-modes (MZMs) with a finite lifetime in the presence of
dissipation. Most interestingly, dissipation can also generate two kinds of
dissipative boundary states: four robust zero-modes (RZMs) and two MZMs, in the
regime where the non-dissipative system is topologically trivial. The MZMs
appear via bulk gap closing and are topologically characterized by a winding
number. The RZMs are not associated with any bulk states and possess no winding
number, but their emergence is instead tied to exceptional points. Further, we
confirm the stability of the dissipation-induced RZMs and MZMs in the presence
of random disorder. Our study paves the way for both realizing and stabilizing
MZMs in an experimental setup, driven by dissipation.
