  The notion of Self-organized criticality (SOC) had been conceived to
interpret the spontaneous emergence of long range correlations in nature. Since
then many different models had been introduced to study SOC. All of them have
few common features: externally driven dynamical systems self-organize
themselves to non-equilibrium stationary states exhibiting fluctuations of all
length scales as the signatures of criticality. In contrast, we have studied
here in the framework of the sandpile model a system that has mass inflow but
no outflow. There is no boundary, and particles cannot escape from the system
by any means. Therefore, there is no current balance, and consequently it is
not expected that the system would arrive at a stationary state. In spite of
that, it is observed that the bulk of the system self-organizes to a
quasi-steady state where the grain density is maintained at a nearly constant
value. Power law distributed fluctuations of all length and time scales have
been observed which are the signatures of criticality. Our detailed computer
simulation study gives the set of critical exponents whose values are very
close to their counter parts in the original sandpile model. This study
indicates that (i) a physical boundary and (ii) the stationary state though
sufficient but may not be the necessary criteria for achieving SOC.
