But it was for a sick kid
It’s BECAUSE it’d be for a sick kid that makes it make the most sense. Based on simply a value system, that’s why they didn’t give him medicine. He would be essentially a “drain” on the town since he can’t provide any goods or services to keep his worth. Looking down the line he would be able to provide something of value when he grew up, but it’s a cost benefit analysis of what he can provide eventually, and what he’s taking now. If he takes the medicine and then one of the people who is giving the town supplies died because of that, it would be a net negative for the town as they still have an additional mouth to feed that is reaping them no benefits, and less goods coming in. I’m not saying that it’s morally right, but based on them being in survival mode during a zombie apocalypse, it makes sense for the town to have a punishment for something like that. Death seems pretty harsh though. It might be a way to maintain groupthink in the community, which in some cases can be considered to be more beneficial than what one individual person can provide.
I'm not condoning what they did was right but I am looking at logical perspective when resources are running low and someone steals they should somewhat get punish but not death. We also need remember this is setting where it's pretty much the apocalypse. It's either we risk it all for one person and everyone dies or we make sacrifices to keep everyone alive. You can't take any chances when it comes to survival. However, in this case how they went about it was messed up. It does make you question do you choose your morals or you put your feelings aside and do what is right for the greater good because at the end of the day everyone is just trying to survive.