たなり says someone did something and then stayed that way, when you would expect something else to follow: went out and never came back, sat down and didn't move. The verb is in the た-form, and the second half is usually negative.
There is often a note of complaint or worry that the situation has not changed.
After the dictionary form, なり is a different pattern meaning "as soon as". The form of the verb is the only thing that tells them apart.
Two dictionary forms each followed by なり, as in いく行くなりかえる帰るなり, are a third pattern: "either X or Y".
たなり is literary; you meet it in novels and essays. In speech the same idea is たきり, or たまま for a state left unchanged.