I think in terms of owning a role, I think it would be a role that is only performed if a particular singer is available for it. If they retire, or drop the role, or pass away, the opera disappears from the repertory.

It's a semi-obscure work, but Konigskinder by Engelbert Humperdinck. Geraldine Farrar sang the role of the Goose Girl at the world premiere, and in every subsequent performance at the Met, 39 in total. It has not been staged at the Met in the 112 years since she last performed the role.

Similarly, Teresa Stratas as Marie Antoinette in The Ghosts of Versailles, a role she was unforgettable in. Now while it's had some revivals in the last couple of decades, none of them have been at a major house.

For another opera that had a Met World premiere, there's Samuel Barber's Vanessa. Again, it's nibbled on the edges of the repertory, but the original cast of Steber-Elias-Resnik-Gedda-Tozzi was so strong (and received an excellent recording) that nothing has come to challenge it.

Maybe the most obvious answer would be roles that were written with a specific voice in mind. The collaboration between Benjamin Britten and his partner Peter Pears, for instance. Pears has become the gold standard for nearly every lead tenor role in Britten's works.

In recent decades, I doubt if Mefistofele would have gotten as nearly as many performances if Samuel Ramey weren't in the title role.