In this paper, the Optional Prisoner's Dilemma game in a spatial environment, with coevolutionary rules for both the strategy and network links between agents, is studied. Using a Monte Carlo simulation approach, a number of experiments are performed to identify favourable configurations of the environment for the emergence of cooperation in adverse scenarios. Results show that abstainers play a key role in the protection of cooperators against exploitation from defectors. Scenarios of cyclic competition and of full dominance of cooperation are also observed. This work provides insights towards gaining an in-depth understanding of the emergence of cooperative behaviour in real-world systems.