So the problem shifts from corruption to affordability. The free food program exists because they can't afford it. If we can fix the affordability problem, there won't be a need for a free food program and there by corruption related to it won't exist.
These people need to get jobs. But since they don't have it. You may by all means fix corruption and give them free food, but they will hungry again in the next six months. Where will you get free food from, then and till when?
IIRC Mr. A. Sen won the nobel for showing that people starved not because of lack of food, but because of lack of purchasing power.
The wiki page suggests that his findings are being debated though, to be fair.
My google foo is also a bit literal at the moment, and I wasn't able to produce a result which explained what he won his nobel for.
The subsidy/pds is supposed to shift the price of goods down, so corruption does affect the intended price of goods by making them unavailable at the subsidized rate.
That's why I chose the supply curve. Correct me if I got it wrong.
Demand shifts of course (the overall price of the product drops because the stuff that wasn't supposed to make it to the market gets there, but free stuff disappears -> structure changes).
The supply curve is the amount of goods produced at x price.
Since x isn't being changed here for sellers, it doesn't move.
The demand curve does move because of the distorting effects of the subsidy/PDS, and then again because of corruption.
That is a simplification. It is both being stolen and it is rotting.
Even the article states that there is tons of food that is rotting/wasting away. If it doesn't mention it, I can give examples of food stock being wasted from as long back as, I think 1970-1980.
Also - Corruption DOES shift the supply curve so "corruption does not change supply and demand" is only true in the land of platonic ideals.