No, no, no, no; and yes, if you really need to count references you will have to do it manually. JS has no interface to this, GC, or weak references.
Whilst you could implement a manual reference-counted object list, it's questionable whether all the extra overhead (in performance terms but more importantly code complexity) is worth it.
In your example code it would seem simpler to forget the Repository, use a plain Array for your lists, and let standard garbage collection take care of dropping unused people. If you needed to get a list of all people in use, you'd just concat the friends and coworkers lists (and sort/uniquify them if you needed to).