If you have a valuable artifact that you don't have on display, renting it for a large sum to someone is a reasonable thing to do. Of course it goes without saying that you ensure whoever gets it takes care of it. Better it be on display at a rich person's house where I might get an invite to see it than in the basement where nobody can see it.

As has been noted museums tend to be on the brink of financial insolvency. Getting a rich person to rent some art is a valid way to get enough money to stay solvent and continue to provide art to others. There is a lot more great art worth preserving than there are museums in the world.

Note, the above is not a comment on IF it is done. I have no idea if it is possible for someone to actually do this.