Suppose you were liable to be called away at a moment's notice – for a long time – and you couldn't take pets along. What if you suddenly got that chance to go to the Antarctic and inspect its wildlife? (Oh please, National Science Foundation.) Perhaps you hope for a last-minute berth to visit the International Space Station. Or maybe you fear arrest.

In any of these cases, you won't be able to bring beloved animals. You may have made tentative arrangements. "Will you keep Tag if I go to McMurdo? Just don't give him too much water late at night." "If I get the nod, I'll take Hairball to the launch site and hand her over to you in the parking lot, okay? Just put your houseplants up high." "If they don't grant bail, can I count on you to take the piranha tank? Just don't put your hand in the water."

But what if you are a fundamentalist Christian who believes in the Rapture? Specifically, if you believe you will be Raptured prior to a period of tribulation? (Some argue Rapture will occur after Tribulation.) Animals are said to be ineligible for Rapture. (Ecclesiastes 3:21, for example, refers to "the spirit of man that goeth upward, and the spirit of the beast that goeth downward to the earth".)

What will become of your pets when you are snatched up to heaven? Really bad stuff is predicted to happen during Tribulation. How safe will a small fluffy dog be? Who will look out for the interests of an indoor cat, a tank of fish who actually have quite narrow temperature requirements, or a bird with only a few words of English?

Post-Rapture Tribulationists in the United States have a possible answer. Eternal Earth-Bound Pets, USA, is staffed by avowed atheists, also ineligible for Rapture. For a one-time charge of $110, they pledge to adopt your pet if you are Raptured within the next 10 years. Founded in June 2009, they now cover 22 states.

I called Eternal Earth-Bound Pets (EEBP) and spoke to co-founder Bart Centre. Under the name Dromedary Hump, Centre has a blog, The Atheist Camel, and has self-published The Atheist Camel Chronicles: Debate Themes & Arguments for the Non-Believer (and those who think they might be). He's a retired executive, and "a lifelong activist in the culture war between theist demagoguery and free thinkers."

Centre is emphatic that the offer is not a hoax. "It's a very serious offering," he says. "We're not poking fun. We're saying in very clear language that we do not believe, but if we're wrong, and you're right, then we're here." Representatives (who will adopt pets in the event of Rapture) are screened carefully. "They're atheists known to us personally as friends or relatives."

Centre says the notion originated in a chapter of The Atheist Camel Chronicles in which "I mused over the end time theology ... and asked how could I make this into a business venture?"

There could be a large market. "There are 40-50 million believers in the Rapture in this country," Centre says. He hasn't been able to learn how many think Rapture will precede (not follow) Tribulation. "Say the target market is 20—40 million people."

How's business? Email is pouring in, "more debates than customers," Centre says. "We have gotten thousands of emails from atheists congratulating us on this wonderful joke. But it's not a joke." That's 85% of the email. Ten percent comes from angry or reproachful Christians. "Five percent are people who take it seriously, who have had this on their minds. They're feeling us out."

In November EEBP announced their 100th client, the first in New England, Centre's territory. "I'm happy to be able to assure our latest client that her pups will be part of my family, and in good company, should the Rapture take her over the next 10 years."

That's not very many. Don't Rapture believers care about animals? Jerry B Jenkins, co-author of the Left Behind series, waffles about pets. In The Authorised Left Behind Handbook he says the Bible doesn't deal with the issue. "People always ask me, 'Is my dog going to be raptured?' 'Will I see my cat in heaven?' There is imagery of animals in heaven, but we don't know if they are our personal pets." Jenkins wouldn't want you to think the books don't mention animals. During Tribulation earthquakes, "We see dogs running in circles and roadkill-type animals running across the street." ("Roadkill-type animals?" I'm not having Jenkins watch my pets this weekend, let alone during a Tribulation.)

Some experts opine that animals are pleasant company, so while soulless pets can't be saved, there may still be animals in heaven, fungible furry friends. Yet it would seem logical for believers to worry about the fate of particular beloved pets.

"I actually did think it would be a larger initial response," Centre says. Why haven't more people signed up? "There's a very good reason why. They don't trust atheists ... They see us as immoral and untrustworthy." When correspondents raise this issue, "I remind them of the good Samaritan that Jesus spoke of. So one does not have to have belief in the God of Abraham to be a good person."

Believers might also have read Centre's blog and noted his tendency to refer to people much like themselves as "sheeple." But if they read thoroughly he will seem less hostile to believers. He appears to be on good terms with his "much-put-upon Episcopal wife."

If EEBP's market was originally conceived of as post-Rapture Tribulationists, it now appears narrower: post-Rapture Tribulationists who love particular pets, and who can bring themselves to trust atheists.

While the number of customers for Rapture insurance has disappointed, the site has gotten a gratifying amount of publicity. EEBP sells ancillary merchandise – T-shirts and tote bags – through Cafe Press. Publicity also boosts The Atheist Camel Chronicles. Centre is delighted to find the book "in the top 20 of Amazon's atheist list. I'm right up there with Dawkins and Hitchens and all the big names."

As for the core business, perhaps sales are about to spike. It's the perfect gift for every pet-loving post-Rapture Tribulationist on your list. If you get it for them, they don't have to worry about whether to trust atheists. What else are you going to get them, a headstone?