I've often heard public lectures describing the degenerate, exotic matter left behind after a star collapses but fails to go supernova; one that has found its way to become a neutron star. The speaker will often describe a tablespoon of the exotic material consisting mainly of neutrons, weighing hundreds if not thousands of tons.

It seems to me what keeps such degenerate material stable is the whole gravitational force of the neutron star, but I realize I may be wrong. Perhaps it's reached a state of stability under its own forces once the force of gravity created this exotic matter?

So hypothetically speaking if one could scoop up a tablespoon of neutron soup from the collapsed star, transport it back to earth, and somehow contain its extreme weight, would the matter remain stable - or would it fly apart?