Damselflies have four wings that are controlled independently during flight. The fore and hindwings typically beat out of phase and the interactions which enhance or attenuate flight forces of the wing pairs is phase dependent. During oviposition, however, there exists a species (Neurobasis chinensis) that flies by beating only the forewings while the hindwings are kept outstretched and stationary. Using computational fluid dynamics simulations and high-speed photography, we examined the aerodynamics of this unique flight behavior. We hypothesized that the hindwings passively extract energy from the wake of the forewings without moving. To test our hypothesis, we modeled this behavior first at a two-dimensional level using two airfoils; one flapping and the other fixed at different angles of attack. Then we extended our analysis to three-dimensions using three-dimensional reconstructions of real footage of a damselfly in free forward flight, and performed a similar study. Our findings elucidate the interactions between a flapping and stationary wing and add to our understanding of insect flight which serves as an inspiration for improving and developing micro-aerial vehicle design.