  We consider the activated random walk (ARW) model on $\mathbb{Z}^d$, which
undergoes a transition from an absorbing regime to a regime of sustained
activity. In any dimension we prove that the system is in the active regime
when the particle density is less than one, provided that the jump distribution
is biased and that the sleeping rate is small enough. This answers a question
from Rolla and Sidoravicius (2012) and Dickman, Rolla and Sidoravicius (2010)
in the case of biased jump distribution. Furthermore, we prove that the
critical density depends on the jump distribution.
