Does the property have the right to prevent the lessee from taking things without paying management fees?

The property has no right to stop you from handling your own things. You can move and sell, but they have no right. Just after the police said that owing property fees was an economic dispute, they would not let people go to court, which violated their freedom of activity and was not allowed by law.

Personal experience. When the police came, the security guard softened. I suggest you call the police. (Location: Shanghai) Not familiar with other cities.