Suppose Aaron leaves something in a public place, where people often leave such things without intending to forfeit them. Baruch then puts a sign on the item indicating that it's forfeit and whoever wants to can take it. Gideon then consumes, damages, or simply takes the item.
What is the degree of responsibility of Baruch and of Gideon to restore the item, or its value, to Aaron?
(I can imagine that the answer may possibly depend on the credibility of the sign. I imagine it may also possibly depend on whether the item is intact. And it may possibly depend on other factors. I'd appreciate if any answer would indicate which such factors are relevant and how.)
 Possible examples are a car in a parking spot on the street and food in a workplace refrigerator. But perhaps those examples don't work well with the rest of my question, and you shouldn't restrict your attention to them.