If you're talking about possessions:
* Liability: This refers to something that is a financial burden or responsibility, the opposite of something you own.
* Debt: This is a specific kind of liability where you owe money to someone.
* Nothingness: This refers to the state of not having anything at all.
If you're talking about a characteristic or quality:
* Defect: This refers to a flaw or imperfection, the opposite of a desirable quality.
* Shortcoming: This is a weakness or deficiency.
* Lack: This means the absence of something, the opposite of possessing a quality.
If you're talking about real estate:
* Common area: This refers to land or buildings shared by multiple people, like in an apartment complex.
* Public domain: This is land or resources owned by the government, the opposite of private ownership.
For a more precise antonym, please provide more context about how you are using the word "property."