We had a run on food as well. What happened is that we prioritised food delivery, with in some instances the support of the army IIRC. Something we understandable were not willing to do for toilet paper.
There is a simple reason for that: you cannot have a functioning country if there is a famine and governments will do everything they can to keep a grip on their country.
If it comes to this, having a well stocked pantry becomes the least of your worries as you now have to defend it against your starving neighbours. They won’t be deterred by tough guy smugness.
It’s a good idea to have stocks because it helps mitigating short-term price spikes or unforeseen circumstances such as an accident. Not having stocks won’t cause anyone to starve.