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Suppose that a person buys a packet of sugar. On the way home, the packet falls off his hands and the sugar scatters on the ground. Nobody is expected to gather the sugar again, but that person does so; of course not for his own use anymore, but to donate it to the poor!
Obviously, if the packet hadn't fallen down, he wouldn't have decided to donate it. It goes without saying that this kind of donation and charity is morally worthless and not considered a good deed.
Is there any English idiom to describe this kind of charity or donation?
Thanks in advance.

castoffs

The type of charity described in the original question occurs on a country-wide scale sometimes. Recently, an EU member donated a large shipment of medicines to our local General Hospital; however, when it came time to distribute them, it was realized they were already expired.

There is a word to describe this type of donation of unwanted materials: they are cast-offs.

things, usually clothes, that you no longer want:

-Cambridge Dictionary online

Cast-offs usually refers to old clothes which are given to poor relations or dumped in those large bins outside churches in the US, but the word could also be used to describe any unwanted item that is given away. A synonym is reject.

Cast-offs are not usually rejected for being out-of-date in the third world: here old clothes are sold in Mega-pacas and clothe the majority of the poor people.

By way of contrast, I heard that some US food chains are donating what they used to call “waste”:

...food that passes the restaurant-issued freshness date but is still entirely wholesome and edible by FDA standards is packaged, labeled and sent off to community organizations that feed the hungry, such as after-school programs, day cares, transition homes and rehabilitation centers.

Some seek to go even further, donating left-overs and table gleanings.

“Demeaning” depends on your point of view. The morality of charity is not always clear-cut, but hunger has its own politics.

The only idiom that I can think of is One man's trash is another man's treasure which means:

Prov. Something that one person considers worthless may be considered
valuable by someone else.

[McGraw-Hill Dictionary of American Idioms and Phrasal Verbs]

salvage describes both the OP and the comment scenario. You rescued the sugar from waste, and extracted some residual utility if not your full value. Same with the evening duration with girlfriend or brother: you rescued it from waste, and extracted some residual utility if not your full value.

Miriam-Webster salvage

• the act of saving something (such as a building, a ship, or cargo) that is in danger of being completely destroyed




• something (such as cargo) that is saved from a wreck, fire, etc.




• something extracted (as from rubbish) as valuable or useful

The man offloaded the dirty sugar by donating it to the poor.

to offload — (transitive) to get rid of things, work, or problems by passing them on to someone or something else.
He offloaded the defective car onto an unsuspecting buyer. – Meaning #2 from
https://en.m.wiktionary.org/wiki/offload

There's a neologism, not in any dictionary, that's gaining traction and that is "freecycle".

Rather than dispose of something unwanted, you freecycle it and someone who wants it takes it off your hands.

It has, in large, been driven by the freecycle website.

_{I have no affiliation with said website.}

Not sure if this is widely used but I think it would be widely understood if you identified this act discarding to charity or charitable discard

In the "British Dictionary definitions" section for discard it reads:

1. (transitive) to get rid of as useless or undesirable

If you add the element of deception to the mix then you can say pawn-off to charity

pawn-off

http://idioms.thefreedictionary.com/pawn+off

To get rid of or dispose of something deceptively by misrepresenting its true value.