Exactly. Resources are limited, so a person's rights to personal property must always traded-off with others persons' rights to live in dignity or being able to live at all. Otherwise you'd have to accept the case that the personal rights of property of a few can essentially deny the right to live in dignity or live at all to others whenever resources are distributed in an extreme way to only those few.

In case you're interested, there are quite elaborate theories of distributional justice. For example, New Theory Of Fairness And Social Welfare by Marc Fleurbaey and Francois Maniquet is a very good recent book on the topic, if you're fine with a decent amount of economic apparatus.