Nuclei, composed entirely of neutrons, are an unsolved problem for theory and experiment. I will present a conjecture about the existence of such a bound, pure neutron core whose characteristic is the absence of any bound substructure -- removal of an arbitrary number of neutrons from this core leads to the disintegration of the object in single, free neutrons. As such they present a generalization of the so-called Borromean structure as an emergent property of the nuclear interaction in helium-6. The conjecture is motivated, in part, by QCD simulations which find a bound di-neutron if the quark masses are detuned to larger-than-physical values. I will thus present the implications from the mechanism responsible for the multi-neutron bound state for the search for these objects in QCD simulations.