Possessive refers to something that belongs or relates to someone, often indicating a close relationship between two things. It can also describe an attitude or behavior characterized by strong control or desire for something.
Sentences using possessive pronouns generally use other modifiers to point something out and claim ownership. (thoughtco.com)
The G2Z affiliates are «not possessive about their own turf, or «That's not my shelter, so I'm not going to worry about animals that are there.» (animalsheltering.org)