  We study the late-time dynamics of two particles confined in one spatial
dimension and subject to two-body losses. The dynamics is exactly described by
a non-Hermitian Hamiltonian that can be analytically studied both in the
continuum and on a lattice. The asymptotic decay rate and the universal
power-law form of the decay of the number of particles are exactly computed in
the whole parameter space of the problem. When in the initial state the two
particles are far apart, the average number of particles in the setup decays
with time $t$ as $t^{-1/2}$; a different power law, $t^{-3/2}$, is found when
the two particles overlap in the initial state. These results are valid both in
the continuum and on a lattice, but in the latter case a logarithmic correction
appears.
