I guess portfolio is a better word I might use? Like if you ask me to write an interesting API, I could convert it into a project for future work. If you ask me to write a cool script, I could put it into an existing "interesting scripts" repo I maintain.

I have never seen a take-home project yet that I could do this with. Also they come with scary "You may not show this to anyone else, ever!" disclaimers which are more off-putting.