  Topological objects resulting from symmetry breakdown may be either stable or
metastable depending on the pattern of symmetry breaking. However, if they
acquire zero-energy modes of fermions, and in the process acquire non-integer
fermionic charge, the metastable configurations also get stabilized. In the
case of Dirac fermions the spectrum of the number operator shifts by 1/2. In
the case of majorana fermions it becomes useful to assign negative values of
fermion number to a finite number of states occupying the zero-energy level,
constituting a \textit{majorana pond}. We determine the parities of these
states and prove a superselection rule. Thus decay of objects with half-integer
fermion number is not possible in isolation or by scattering with ordinary
particles. The result has important bearing on cosmology as well as condensed
matter physics.
