  F-theory on K3 admits non-BPS states that are represented as string junctions
extending between 7-branes. We classify the non-BPS states which are guaranteed
to be stable on account of charge conservation and the existence of a region of
moduli space where the 7-branes supporting the junction can be isolated from
the rest of the branes. We find three possibilities; the 7-brane configurations
carrying: (i) the D_1 algebra representing a D7-brane near an orientifold
O7-plane, whose stable non-BPS state was identified before, (ii) the exotic
affine E_1 algebra, whose stable non-BPS state seems to be genuinely
non-perturbative, and, (iii) the affine E_2 algebra representing a D7-brane
near a pair of O7-planes. As a byproduct of our work we construct explicitly
all 7-brane configurations that can be isolated in a K3. These include
non-collapsible configurations of affine type.
