We study the energy spectrum and the persistent current in an ideal one-dimensional mesoscopic ring coupled to a fermionic reservoir. We find that the tunnel coupling in general leads to the suppression of the persistent current. However, with increasing coupling, the effective level structure of the ring coupled to the reservoir changes and quasistates with a sharp eigenenergy develop. Depending on the number of ring states coupled to the reservoir this results in a nonzero persistent current even at very large tunneling between the ring and the reservoir.