Using x-ray photoelectron spectroscopy, thermal desorption spectroscopy, and scanning tunneling microscopy, we show that upon keV Xe+ irradiation of graphene on Ir(111), Xe atoms are trapped under the graphene. Upon annealing, aggregation of Xe leads to graphene bulges and blisters. The efficient trapping is an unexpected and remarkable phenomenon given the absence of chemical binding of Xe to Ir and to graphene, the weak interaction of a perfect graphene layer with Ir(111), as well as the substantial damage to graphene due to irradiation. By combining molecular dynamics simulations and density functional theory calculations with our experiments, we uncover the mechanism of trapping. We describe ways to avoid blister formation during graphene growth, and also demonstrate how ion implantation can be used to intentionally create blisters without introducing damage to the graphene layer. Our approach may provide a pathway to synthesize new materials at a substrate - 2D material interface or to enable confined reactions at high pressures and temperatures.