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Where do old costumes go when their shows die? If we’re lucky, to TDF’s Costume Collection, where they’ll surface again in regional productions, high schools, Vogue magazine spreads and the occasional “Saturday Night Live” skit.

TDF — Theatre Development Fund — is best known for its half-price TKTS booths, but it also maintains what may be the world’s biggest closet: a sprawling, 16,000-square-foot space at the Kaufman Astoria Studios. Divided roughly by genre — medieval, Native American, ethnic, “men’s loud” (think “Guys and Dolls”) — some 80,000 costumes and accessories are overseen by a hardy, mothball-resistant staff of six who field requests from around the country.

But they don’t loan their gear, albeit for a fee, to just anyone: Only nonprofits and commercial projects need apply. Halloween parties are out.

More than a dozen of these gems will be paraded at TDF’s 40th anniversary bash Wednesday from 11 a.m. to 1 p.m. in Times Square. Between appearances by theater royals Harvey Fierstein, Julie Halston and the cast of “Forbidden Broadway,” TDF staffers will model some historic costumes, including one of Joel Grey’s (tiny) “Cabaret” tuxedos and Ariel’s wedding dress from that Broadway shipwreck, “The Little Mermaid.”

“We hardly say no to anything,” says director Stephen Cabral, who’s overseen the collection for 20 years. Every dress, belt, sash and tie of it has been donated — not just from Broadway and off-, but from opera, TV and film.

Since most items are custom-made, they’re unsized, so actors sometimes come in for fittings. Often wardrobe people arrive, armed with their cast’s measurements, and are given little red tape measures and hours to roam the aisles. Rentals are on a sliding scale, depending on seating capacity: a small (under 149-seat) theater could get by for $45 a week.

“If only these costumes could talk,” says Cabral, who relies on his memory of who wore what when he leads tours (at $5 a head) through the nonprofit collection’s five rooms.

“We have costumes worn by the Andrews Sisters and Lena Horne, but for younger people, a dress worn by Milton Berle means nothing,” he sighs. “They’re much more interested in an apron worn by Lea Michele on ‘Glee,’ or anything from ‘Wicked.’ ”

In fact, TDF has one costume “Wicked” audiences in New York have never seen: an elaborate negligee for Elphaba’s sister, Nessarose. According to Cabral, it took so long to make that when the show started tryouts in San Francisco, Nessa wore a housecoat. By the time the nightie was ready, director Joe Mantello decided to stick with the coat.

Not all costumes make it here. Hit shows take them on the road, flop shows sell them and a few lucky stars get to keep them — which is why you won’t find Glenn Close’s gorgeous gowns from “Sunset Boulevard.”

But sometimes, Cabral says, the collection scores big.

“We just received the clothes Denzel Washington wore in ‘Fences,’ ” he says of that Tony-winning 2010 revival. Now on display at TDF’s Midtown office, Denzel’s duds will one day join its cousins out in Queens.