For a given countable discrete group, consider a nonsingular (i.e. non measure preserving) Bernoulli shift action with two base points. We prove that, under some assumptions on the group and associated measures, the Bernoulli action is solid. This generalizes solidity in the measure preserving case by Ozawa and Chifan--Ioana, and is the first rigidity result in the non measure preserving case. This is joint work with K. Hasegawa and T. Kanda.