住 (live) belongs to a category of verbs known as 姿势动词 (positional/postural verbs). Other examples include 站 (stand), 坐 (sit), 躺 (lie) and 蹲 (squat). When you negate such verbs, both the 不 and 没 forms are acceptable.
不 often denies a future action.
没 often denies a past action.
Both 不 and 没 can deny a current action.
Both 不是 and 没有 can be a stand-alone answer to a current status.
But here's the nuance:
不住 Maybe I used to live there, but not any more. (Deny the future.)
没住 Maybe I'm not living there for now, but may move in. (Deny the past.)