The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1839-1933) addresses the case of a person who makes a wedding in his backyard (which was common in those days), to which many guests are invited, and somebody finds on the ground money that was apparently lost. Assuming the money was not stacked in a unique and distinctive way, and was not in a wallet or other personal item, the finder may keep the money. Even though the wedding is held in a person’s private property, the setting is considered a public domain with respect to this Halacha, since large numbers of people are present. It can be assumed that the individual who dropped the money immediately despaired from retrieving it since there were so many people in the area. If, however, the money had a distinctive feature, such as if it was found in a wallet or bag that could be identified by the owner, then the finder must announce the find so that the owner could come forward to describe the item and then retrieve his lost money. Since there are Simanim (distinctive features), and the people in the area are Jews, the obligation of "Hashabat Abeda" (returning lost objects) applies. Otherwise, however, if a bill is found lying on the ground, the finder may keep the bill.
The Ben Ish Hai then adds that this applies only if the money is found at a public event. It goes without saying that ordinarily, if a person finds money scattered about on somebody’s private property, such as in his yard or on his porch, and it clearly belongs to the owner of the property, he cannot claim rights to the money that he finds. Even if it is clear that the money was misplaced, the owner did not despair from finding it, since it was lost on his property, where it would eventually be found. Therefore, the money must be returned to the owner.
The Ben Ish Hai rules that a store, where customers are coming in and out, has the status of a public domain with respect to this Halacha. If somebody finds money lying on the ground in the store, he may keep the money, and the storekeeper cannot claim that the money belongs to him. Even though he owns the property, the finder may keep the money, because the store is considered a public area.
Summary: If a person finds money on somebody else’s private property, then generally speaking, he must give it to the property owner. If, however, this occurs when a public event takes place on the property, such as if a wedding is held in somebody’s backyard, the finder may keep the money. If the money had some distinctive feature, such as if it was in a wallet or a particular kind of bag, the finder must announce his find. A person who finds money in a store that has customers coming in and out may keep the money.