Can you own something without a government enforcing that ownership right? Sometimes, yes:
Some time ago I read about Boston’s system for allocating parking spaces in snowy weather: you clear it, you claim it. (See also more recent articles, too.) I happened to see this system in action yesterday for the first time. People not living in areas with proper winter climes might not have heard of this before, and I think it’s a nifty little system worth highlighting. It calibrates investments and incentives, thus “pricing” a scarcity to produce a more efficient allocation. It saves money, because there’s no need to pay city workers to clear spaces. And it does so with little administrative overhead: individuals overwhelmingly maintain the system. It’s a thing of beauty all around.
For more on the economics of this property system, see the article Snow Jobs at the Library of Economics and Liberty.