A post-apocalyptic short story where very sick people from our future save people in our timeline that would be killed in plane crashes

Question

I read this short story about 20 years ago, in a collection that was possibly much older.

Some sickness has almost destroyed mankind and the survivors are sterile, and in the rare cases they can have children, the latter will also be very sick.

On the other hand, a planet similar to Earth has been discovered, and it is possible to send people there. Life is harsh, but there is hope for mankind to survive there. But there is no point sending sick people to die there.

So they have developed a plan. They have records of plane crashes that left no survivors, in their past which is our present. They cannot change the past, so the plane must crash. But they have a time-travel machine that allows them to send operatives on the plane, send all passengers and crew to their time, and replace them by dummies before the crash. So when the wreckage is found, everything will be exactly as recorded.

Answer 1

The John Varley short story "Air Raid" (1977) (that was later expanded into his novel Millennium, and adapted as a movie) seems to fully match your question.

They are grabbing fatalities (and they must have died in the past) from an air disaster:

Flight 128 was mechanical failure. That's the best kind; it means we don’t have to keep the pilot unaware of the situation in the cabin right down to ground level. We can cork him and fly the plane, since there’s nothing he could have done to save the flight anyway. A pilot-error smash is almost impossible to Snatch. We mostly work mid-airs, bombs, and structural failures. If there’s even one survivor, we can’t touch it. It would not fit the fabric of space-time, which is immutable (though it can stretch a little), and we'd all just fade away and appear back in the ready-room.

In the future they manufacture duplicates of the people snatched in order that it appears they died in the crash:

It is a deadening routine. You grab the harness around the wimp’s shoulders and drag it along the aisle, after consulting the seat number painted on its forehead. The paint would last three minutes. You seat it, strap it in, break open the harness and carry it back to toss through the gate as you grab the next one. You have to take it for granted they've done the work right on the other side: fillings in the teeth, fingerprints, the right match in height and weight and hair color. Most of those things don't matter much, especially on Flight 128 which was a crash-and-burn. There would be bits and pieces, and burned to a crisp at that. But you can't take chances. Those rescue workers are pretty thorough on the parts they do find; the dental work and fingerprints especially are important.

The snatched survivors are being sent to colonize a new world:

"...Centauri 3 is hospitable, with an Earth-like climate. By that, I mean your Earth, not what it has become. You’ll see more of that later. The trip will take five years, shiptime. Upon landfall, you will be entitled to one horse, a plow, three axes, two hundred kilos of seed grain..."

I read the story in the Varley collection The Persistence of Vision, but you can read it in the first edition of Asimov's, Spring 1977, at the Internet Archive.