dependent no, they are social constructs given because of logical constructions of individuality. Private property does facilitate it though.
In didn't "facilitate" it on the privately owned southern slave plantations. Indeed, the aristocratic lifestyle of the slave owners would not have been possible without compulsion in that period when "market forces" worked to the advantage of a genuinely free and mobile labor force.
Slavery cannot exist in a world in which all human beings are deemed equal to each other as moral agents, they can only sign voluntary contracts which is not slavery.
HERE is a picture of some sharecroppers, who were identical to their officially enslaved forebears in everything but name:
If someone is worked like a slave, fed like a slave, clothed like a slave, housed like a slave and have no real alternatives except starvation then they are a slave regardless of whether they are LEGALLY "deemed equal" to any other citizen. De facto slavery brought about as a result of such Hobson's choice is not imbued with moral validity because the slave and their exploiter have signed a LEGALLY "voluntary" contract. Theoretical "Freedom of movement of labor" which is not a PRACTICAL REALITY is NO freedom.
Freedom of speech is a given on private property when you can say and do what you want on your own property.
Well the Southern slave plantation owners had the "freedom" to call their slaves things like "nigger". The slaves however did not have the freedom to answer back.
Democracy only depends on the people who approve of it. In that sense private property and the ability to consent to use such property in a communal society is paramount. It is wasn't so then we'd have what we have in the Middle East "Democracies" that mean absolutely nothing.
Most middle eastern countries have private property. So why aren't they democracies?