verb (used without object)
to advance beyond proper, established, or usual limits; make gradual inroads: A dictatorship of the majority is encroaching on the rights of the individual.
to trespass upon the property, domain, or rights of another, especially stealthily or by gradual advances.

1275–1325; Middle English encrochen < Anglo-French encrocher, Old French encrochier to catch hold of, seize, equivalent to en- en-1 + -crochier, verbal derivative of croc hook < Germanic; see crooked, crook

encroacher, noun
unencroached, adjective
unencroaching, adjective

1, 2. See trespass.
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Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
encroach (ɪnˈkrəʊtʃ)
vb (often foll by on or upon)
1.  to intrude gradually, stealthily, or insidiously upon the rights, property, etc, of another
2.  to advance beyond the usual or proper limits
[C14: from Old French encrochier to seize, literally: fasten upon with hooks, from en-1 + croc hook, of Germanic origin; see crook]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin & History

early 14c., from O.Fr. encrochier "seize, fasten on, perch," lit. "to catch with a hook," from en- "in" + croc "hook," from O.N. krokr "hook." Sense of "trespass" is first recorded 1530s. Related: Encroached; encroaches; encroaching.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
For years, he has watched it encroach from the shores that face the sound and
  the sea.
Opponents say the law will encroach on privacy and jeopardize civil liberties.
As a result, they sometimes encroach on territory private-equity firms consider
  their own.
They will not encroach on technology and medicine.
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