Property (as in property theory) is an intangible abstraction (concept) that describes preferred human action in relation to the subject of ownership (the owned object).
Responsibility of Others
If property were once face on a coin, the other side is the abstraction/concept of responsibility. The type of "implicit" responsibility inherit in "property" depends on the type of property norms one is referring to. For example an ownership norm tends to include (a) priority over use and control (as most perceive property), but also (b) another set of norms regarding the actions of other humans and non-interference with that ownership (i.e. "don't steal or break other's property").
Responsibility of Owner
The above is obvious enough to most, but there's one more aspect of responsibility typically not explicitly explored often. If all 'benefits' of property were attributed to "the owner" and all 'costs' and responsibility was attributed to "non owners," such a system would be highly imbalanced. Instead, balanced ownership norms would show preference to ownership and responsibility of both the benefits and costs of one's actions.
Non-Ownership and Non- Responsibility
The inverse of the above concepts tends to also be true; non-ownership and non-responsibility are commonly linked. Norms which undermine ownership or promote non-ownership, also undermine responsibility and promote non-responsibility. If norms dictate that one may not own the positive results of one's actions, consistent with that is that one doesn't own the negative results either.
The above pursues and promotes the values of balance, ownership, and responsibility and explores the links between those values. The above is however not intended to be used as "objective argumentation" nor preclude the possibility of alternatives, or other values that may (in the right some circumstances) supersede the above values.