Token holders legally have ownership of Lofty properties. When you purchase tokens in a Lofty property, you are directly buying a membership interest in the individual DAO LLC that owns the property.
For example, if you purchase 1% of the tokens in a single home offering, you would then be entitled to 1% of the economic interests of the asset over time, which may include income from rent or property value appreciation.
You can view the DAO LLC Agreements, Closing documents, Deeds, and much more for all properties by going to the "Documents" tab of any property page, and clicking the available link.