It is well known that a simple, supercritical Bienaymé-Galton-Watson process turns into a subcritical such process, if conditioned to die out. We prove that the corresponding holds true for general, multi-type branching, where child-bearing may occur at different ages, life span may depend upon reproduction, and the whole course of events is thus affected by conditioning upon extinction.
"General branching processes conditioned on extinction are still branching processes." Electron. Commun. Probab. 13 540 - 547, 2008. https://doi.org/10.1214/ECP.v13-1419