At this time Kathy, I believe the only resolution to your problem is to contact that cousin.
If you know how they are listed on their Profile, do a search to find them. They can't be unlisted as I believe by being a member you agree to being listed, though you do have Privacy Controls over how much information is revealed. If their Privacy Level permits it, you can look at their Contributions to see how long ago they last did anything on WikiTree. And you can Private Message them as well.
If Active, ask to be on their Trusted List and this will permit you to see the Unlisteds they have added. Also, you can reciprocate by putting them on your Trusted List
Another, but more tedious way, is to click on your father's last name in his Profile. All Unlisteds will show up in the Name List with their Profile Manager's name. You can scroll through the list to see if your cousin's name appears as a Manager. If a common LNAB, tedious may be an understatement.
There may be other work arounds and would like to know if there are myself.