If you mean someone that was your friend, you UNfriened them, and now you just want to re-add or re-friend them? Then YES, why not? as long as they didnt block you.
If that is not what you were asking then please clarify.
it sounds like he might have blocked you...
When you find him through Likes common with your cousin, are you able to click his picture, or does it have an unclickable grey-man-shadow picture? If so, you're blocked.
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