As far as I know, a Wigner crystal could be formed spontaneously from a free electron "cloud" with the right conditions (low temperature and electron density). Would it be stable and not susceptible to being separated through the mechanism described here?:
G. Schmidt, Physics of High Temperature Plasmas (2nd ed.), pg. 72*
And if it would be susceptible to being destabilized, would it be stable if the system had minimal energy?
No, Wigner crystals have net negative charge and the electrons repel each other - it will fly apart without a confining force, as the Schmidt virial argument shows. So you need to add a confining force, whether gravity (but self-gravity is not enough for electrons) or an external field.
In a theorist's notebook, the Wigner crystal phase can be stable with apparently only interacting electrons and nothing else in the model. The trick is to take away the notion of "expansion" altogether, and you are immune to the mechanical instability.
You either have:
But 1 is equivalent to a confining potential, and good luck realizing 2 and 3 in real world.
To follow up on the point made by T.P. Ho (I can't "comment" because I've only just joined and don't have the "reputation") you can make a stable Wigner crystal on the surface of a closed surface such as a sphere (point 1 above) where there are a collection of freely moving charged points on the surface of the sphere. The resulting distribution may have more than one (it usually does) energy minimum, depending on the number of points. The distribution closely resembles a "stealthy hyperuniform distributions" on the surface and a Tammes distribution (the latter which maximises the minimum distance between N points).
