There are a variety of phrases and words that can be used to convey the meaning of "encroached on." Some possible synonyms include "intruded upon," "invaded," "trespassed," "overstepped," "usurped," "infringed upon," "violated," and "appropriated." Each of these terms has slightly different nuances and connotations that may be more or less appropriate depending on the context in which they are used. However, all of them share a common theme of one entity or person taking up space or resources that rightfully belong to another, often causing conflict or tension in the process.