  Balanced gain and loss renders the mean-field description of Bose-Einstein
condensates PT symmetric. However, any experimental realization has to deal
with unbalancing in the gain and loss contributions breaking the PT symmetry.
We will show that such an asymmetry does not necessarily lead to a system
without a stable mean-field ground state. Indeed, by exploiting the nonlinear
properties of the condensate, a small asymmetry can stabilize the system even
further due to a self-regulation of the particle number.
