This is the 7405th most frequent Japanese word.
住み着い
"住み着い" is not a valid Japanese word. You may mean "住み着く," which means "to settle down" or "to take up residence."
Here, '住み着いた' indicates the action of settling permanently in a particular place.
彼は廃屋に住み着いた。
He settled in the abandoned house.
In this sentence, '住み着いた' describes stray cats that have taken up residence in a specific area.
街に住み着いた野良猫が増えている。
The number of stray cats settling permanently in the town is increasing.
'住み着く' in this case is used in the future context, implying a decision to start living in the new area.