  We derive the quasiparticle picture for the fermionic logarithmic negativity
in a tight-binding chain subject to gain and loss dissipation. We focus on the
dynamics after the quantum quench from the fermionic N\'eel state. We consider
the negativity between both adjacent and disjoint intervals embedded in an
infinite chain. Our result holds in the standard hydrodynamic limit of large
subsystems and long times, with their ratio fixed. Additionally, we consider
the weakly-dissipative limit, in which the dissipation rates are inversely
proportional to the size of the intervals. We show that the negativity is
proportional to the number of entangled pairs of quasiparticles that are shared
between the two intervals, as is the case for the mutual information.
Crucially, in contrast with the unitary case, the negativity content of
quasiparticles is not given by the R\'enyi entropy with R\'enyi index 1/2, and
it is in general not easily related to thermodynamic quantities.
