  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.
