Before revision:  The conditions on rate constants that result in networks with SDB but without DDB are stringent, and thus examples of this phenomenon are rare, a notable exception to this is a network whose stochastic model is a birth and death process.
After revision:  The conditions on rate constants that result in networks with SDB but without DDB are stringent, and thus examples of this phenomenon are rare, a notable exception to this is a network whose Markov chain is a birth and death process.