We study the energy spectrum and the persistent current in an ideal one-dimensional mesoscopic ring coupled to an external fermionic reservoir. The contact between ring and reservoir is described by a tunneling operator, which causes an indirect coupling between different ring states via states in the reservoir. For strong coupling to the reservoir new quasistates with sharp eigenenergies develop inside the ring. The formation of long-living states at strong tunnel coupling to the reservoir is analogous to the Dicke effect in optics, this was recently investigated in context of resonant scattering and resonant tunneling in solid-state systems. Our model reproduces the results obtained in previous works based on the scattering matrix approach. Moreover, it describes a stable energy spectrum in the limit of strong coupling that has not been obtained previously.