残り物の私 is the standard way to say this. 残り物な私 is not a typo, but a nonstandard yet somewhat humorous way of saying the same thing. I don't think there is a name for this rhetorical technique where an ordinary noun is temporarily employed as a na-adjective, but it's a tactic you'll occasionally see in creative writing. Essentially, this is done to make a phrase sound informal, interesting and/or humorous by using words in a slightly unconventional way.
Similar examples used in titles:
- ボードゲームな夜
(ボードゲームの夜 is more "standard", but it's uninteresting)
- クレオパトラな女たち
("Cleopatraic Women"(?) クレオパトラの女たち would mean something totally different)
- シュガーな俺
(This title is intentionally made to be puzzling, but those who read it would notice some unique meaning is hidden)
Sometimes, employing a noun (or no-adjective) as a na-adjective can also evoke some derived meaning. For example, see ピンクの vs ピンクな and 無垢の vs 無垢な.