Continuous time markov Chain Intensity Matrix + Steady State

Question

For the continuous time markov chain, the rate matrix Q can be defined with diagonal elements $$Q_{ii}=-\sum_{i\neq j}Q_{ij}$$ My question is this. Since the stationary distribution is defined such that $Q\vec{\pi}=0$ and the matrix Q is defined as above, is there any situation in which $\pi$ is not just defined as $\vec 1$?