First of all, God knows best if this narration/story is true.

But it goes like this.

On the Day of Judgement, people will be so scared about their own fate that they won't even care about the people who were close to them. A mother will run away from her child. A husband will run away from his wife. A brother will run away from his brother. Every one will only care for themselves on that day because they are fearful of their destiny whether they will go to Heaven or Hell.

Everyone's deeds will be placed on the scales and if the good deeds outweight the bad, then they will go to Paradise and vice versa (oversimplified but that's the gist of it).

Now some people will have equal good deeds to bad deeds. So God will tell them if they can find one person to give them a single good deed, then they can go to Paradise (imagine good deeds are like currency and you just need a single penny/cent).

So this person will go to his mother, his father, his spouse, his children, his friends etc. And every single one of them will reject him and not even give away one good deed of theirs because they fear they will need it more.

And at the same time, there will be a person who only has a few good deeds to his name and a lifetime of sins. And he already knows this. He already knows his fate is the Hellfire. So he will see the man who needs a single good deed and he will give it to him because he knows it will make no difference to his own fate. Now the first man has enough to go to Paradise.

But God will also forgive all the sins of the person who gave it away and cause him to go to Paradise too.

Well, that's the story - how I heard it. Again, God knows best if it's true or not.