Is it permissible for the Murabit (those stationed at border outposts) to eat from what is in the abandoned houses near him or from the trees around him, knowing that these properties belong to known individuals?

The default rule is the prohibition of a Muslim's property unless it is given with his willing consent. An exception to this is eating from orchards and drinking from the milk of livestock after seeking permission from its owner three times. If there is no response, one may eat and drink without taking provisions or carrying anything away. As for one who is compelled to eat from another's property, it is permissible for him to do so only to the extent necessary to satisfy hunger and preserve life.