In Borromean nuclei, three separate parts of the nucleus are bound together in such a way that if any one is removed, the remaining two become unbound. The expression originates from the Borromean Rings which consist of interlocking rings.
C12, in its excited state, is one example of a Borromean nucleus. It consists of three sub-units of He4. If one is removed, the result is Be8 which is not bound. Other examples are He6, Li11, Be14, and C22. Borromean rings provide an analogy for the structure of halo nuclei in which the removal of any one of the three major components breaks the whole system.
See also Unbound nuclide
J. Magill and J. Galy, Radioactivity Radionuclides Radiation Springer Verlag, 2005
J. Magill, G. Pfennig, J. Galy, Karlsruhe Nuclide Chart, 7th Edition, 2006.