It’s probably not one of the wisest things to do after a breakup. Even if it was a mutual decision, buying your ex a gift may look like a feeble attempt on your part to make peace with a pity package.  However, having said that, we realize that relationships differ from person to person and so, if you and your ex were really close at one point in time and there's still a lot of concern for them, then perhaps a care package genuinely wishing them well along with a note, may not be completely out of place.