Judging from the context, the Lors will keep the souls of the good and cast away the souls of the wicked
that's my take on it

food for the soul

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Note added at 8 mins (2004-04-22 17:11:56 GMT)
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will not suffer the soul of the righteous to famish: will not allow the souls of good people to be deprived

This is an excerpt from Matthew Henry's commentary on Proverbs 10:3

These two verses speak to the same purport, and the latter may be the reason of the former. 1. That wealth which men get unjustly will do them no good, because God will blast it: Treasures of wickedness profit nothing, Proverbs 10:2. The treasures of wicked people, much more the treasure which they have made themselves masters of by any wicked people, by oppression of fraud, though it be ever so much, as a treasure, and laid up ever so safely, though it be hidden treasure, yet it profits nothing; when profit and loss come to be balanced the profit gained by the treasures will by no means countervail the loss sustained by the wickedness, Matthew 16:26. They do not profit the soul; they will not purchase any true comfort or happiness. They will stand a man in no stead at death, or in the judgment of the great day; and the reason is because God casts away the substance of the wicked (Proverbs 10:3); he takes that from them which they have unjustly gotten; he rejects the consideration of it, not regarding the rich more than the poor. We often see that scattered by the justice of God which has been gathered together by the injustice of men. How can the treasures of wickedness profit, when, though it be counted substance, God casts it away and it vanishes as a shadow? 2. That which is honestly got will turn to a good account, for God will bless it. Righteousness delivers from death, that is, wealth gained, and kept, and used, in a right manner (righteousness signifies both honesty and charity); it answers the end of wealth, which is to keep us alive and be a defence to us. It will deliver from those judgments which men bring upon themselves by their wickedness. It will profit to such a degree as to deliver, though not from the stroke of death, yet from the sting of it, and consequently from the terror of it. For the Lord will not suffer the soul of the righteous to famish (Proverbs 10:3), and so their righteousness delivers from death, purely by the favour of God to them, which is their life and livelihood, and which will keep them alive in famine. The soul of the righteous shall be kept alive by the word of God, and faith in his promise, when young lions shall lack and suffer hunger.

whatever it is, that gives the wicked, its identity.