You asked

how might we apply the 'forgotten sheaf' principle to modern economic and social systems?

The passage, plainly, with room to sit with it.

Deuteronomy 24:19

“When you reap your harvest in your field, and have forgotten a sheaf in the field, you shall not go again to get it. It shall be for the foreigner, for the fatherless, and for the widow, that Yahweh your God may bless you in all the work of your hands.”

This passage is part of Moses's address to the Israelites as they prepare to enter the promised land. It outlines various laws and social regulations intended to establish a just and compassionate society, including provisions for the vulnerable within their community.

How does the idea of leaving provisions 'by accident' challenge our approaches to intentional charity or systemic redistribution?

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Read alongside it

Leviticus 19:9-10
Another command to leave part of the harvest for the poor and foreigners, explicitly including grapes and olives.
Ruth 2:2-3
Shows the practice of gleaning in action, as Ruth gathers grain in Boaz's field.
James 2:15-16
Emphasizes that faith without practical acts of care for the needy is insufficient.

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