To settle in a place; to take up residence and remain there.
野良猫が物置に住み着いてしまった。
A stray cat ended up settling in the storage shed.
彼は大学卒業後、その町に住み着いた。
After graduating from university, he settled down in that town.
あのバンドは東京に長く住み着いて活動している。
That band has been based in Tokyo for a long time.