Is the catholic church a force for good?

[Esquilax]

Justin, Tonus, Esquilax, KichigaiNeko, Rhythm...etc

Can you please help me build a scenario in which an atheist would lay down their earthly life for no reward.
I was hoping for some more detail about motivation and background information.

Yes, easily. I can think of numerous people I would die for in my life, and if dying meant that additional lives could be preserved or saved from danger I would do so easily.

Here's my scenario. A really really devout Christian who wants to follow Christ's example of sacrificial love (because the bible says so,) has given up their whole (adult) life to serve God. They remain celebate and gain their perceived ''purpose in life'' by doing righteous moral actions for the poor and homeless etc etc. No earthly spouse, children. No DNA to pass on. No patriotic loyalty to King and Country (man-made secular government,) This person isnt going to fight in a war because they regard murder/war as immoral. And to nullify the reward/heaven objection, I'm going to characterize them as a person who thinks they are already ''saved'' and laying down their life wouldnt make any difference to their entry into eternal life. Then, one day they have an unexpected opportunity to take the place of someone else in a hostage scenario and they die instead of the original hostage.

Now, their action is motivated by something in the (fictitious) bible, their relationship with God is imaginary according atheists. They gain nothing arising from their action. They dont even want a posthumous statue in their honor and there's no guarantee they would get a statue anyway.

You're missing the point. It's not the reward itself that's in contention; the theist and the atheist in these hypotheticals is just necessarily working under a different set of motivations. Your imagined theist who knows that he is saved is operating under the notion that his death isn't a permanent state, that dying on earth simply moves him up to paradise for eternity. His mortal life is not the end, for him; theoretically he has very little to fear from death.

Conversely, an atheist in the same situation knows that his death is the end, and there is nothing after. His sacrifice is meaningful precisely because he is giving up his continued existence for another, something the theist cannot claim. This conversation has never been about the concrete reality of the reward of heaven, but rather about how the belief in such a thing alters the way a person perceives death. What has a saved theist to fear from death? How is it a sacrifice if they give nothing up and end up better off afterward?

Where is their atheist counterpart? And what motivation lies behind the atheists corresponding desire to take the place of the hostage?

This is an odd question, and I hope you don't mean that you can't think of a reason for self sacrifice at all. That would say a lot of bad things about you. I'll answer anyway; an atheist would sacrifice themselves to save the lives of the other person, because they value life. There's no need for heaven beyond to reward them; the fact that they've helped another person is enough.