I came across posts about sieges and they could last for huge amounts of time. Eventually you'll be starving people out if you're not getting their walls down fast enough.
So those defenders are eating something for a long time. I assume the main food being preserved is grains, because that's historically a pretty safe bet for what people grew, and harvested, and ate.
To keep the scope reasonable, lets limit this to Europe. Who was keeping the food built up? Did food get a treatment before being stored? Did people guard the food from other people inside the walls?
If you're going to be behind your walls for upwards of a year or two, how long was extra grain being built up? Was old grain rotated out, or was there some super ancient grain sitting in the bottom of the barrel forever? Was a surplus always desired in case of sieges, or was it just when you knew there was a war that you started to store extra?
Where can I find more about town-side logistics of medieval sieges?
They still had food preservation techniques back in the day. Salted meat stays edible for a looong time. I haven't read up specifically about grains and such. But I imagine they had plenty of methods for that too. Flour stays good for a long time (years even) if it stays dry and unexposed to contamination.
As far as who stockpiled it, probably the lord who owned the land. Millers payed their taxes in the form of a % of the grain they milled. So these lords would have a lot of grain lying around. They probably sold some. But probably put some into reserves too. They would need the reserves for more reasons than just a siege. If there was a drought, or crop failure, or locusts they might not have enough of a harvest to keep everyone alive, and it would become the Lord's duty to feed his people from his personal reserves.
To the best of my knowledge, stored food that went bad frequently got mixed into feed slop for pigs or goats or whatever.
During a seige it would absolutely be under lock and key. Food was probably the single most important resource to manage during a seige.