Property by itself, however, is subject to use and consumption and therefore diminishes constantly. The most radical and most secure form of possession is destruction, for only what we have destroyed is safely and forever ours. Property owners who do not consume but strive to enlarge their holdings continually find one very inconvenient limitation, the unfortunate fact that men must die. Death is the real reason why property and acquisition can never become a true political principle. A social system based essentially on property cannot possibly proceed toward anything but the final destruction of all property.
It is true that the passage seems surprising - nothing had prepared us for this - and quite muddled. Is it the finiteness of property or of life which poses a problem? Why is the fact that property is subject to use a challenge to property while destruction is an affirmation of it?
At the same time the passage seems to speak the truth, or at least it certainly resonates to me, and reminds us of much about the Nazis - Hitler ordered that Paris be destroyed - and in general - live burial of wives/slaves/horses with prominent dead.
I later came across a similar sentiment in Simone de Beauvoir, more explained. Her argument is essentially that property is a way to alienate yourself - i.e. to project yourself onto the physical world, the other, so as to have an object to grip when you think of yourself. The problem is that in this sense property is impossible - nothing every belongs to anything else, nothing ceases to be what it is which is itself and therefore not yours. Being in a shaky relationship to property, we seek to replace the unattainable with exclusivity. If everyone else acts as though something is yours, i.e. with the respect that they show you, then the ownership at least seems to be true.
Now it is easy to see that the only sure form of exclusivity is through destruction - and it may be that the only true form of property is destruction which is acknowledged to be rightfully done. So what seems to be a paradox - what we have destroyed is not safely and forever ours because it is not - is resolved. It does allow a crack in at the security of destruction-as-ownership, in that people not acknowledging your right to destroy the thing are destroying the social framework that allows you to pretend to ownership - but that will never be actualized in the physical world as it could be by theft before.