When you block or delete people in Snapchat, they are added to the Blocked list. To unblock them, go to the Settings section of the Snapchat application and scroll down to the blocked list. A list with users will be displayed. Tap on the X corresponding to the username you want to unblock. Restart the application and then you can add that friend back.
For additional information, access the following website provided by the developers: https://support.snapchat.com/a/block-friends
