  We study some cases in D=4 and in infinite-volume high dimensional theories
when unbroken supersymmetry in the vacuum cannot guarantee Fermi-Bose
degeneracy among excited states. In 4D we consider an example in which both
supersymmetry and $R$ symmetry are unbroken in the vacuum, and the cosmological
constant vanishes. However, theory admits solitons that do not allow existence
of conserved supercharges. These objects are magnetically charged global
monopoles which in some respect behave as point-like particles, but create a
solid angle deficit which eliminates asymptotically covariantly constant
spinors and lifts Fermi-Bose degeneracy of the spectrum. The idea is that in
some "dual" description monopoles with global topological number and gauge
magnetic charge may be replaced by electrically chaged particles with global
Noether charges, e.g., such as baryon number. Alternatively theories with
infinite volume extra dimensions may support unbroken bulk supersymmetry
without Fermi-Bose degeneracy in the brane spectrum. We suggest a scenario in
which brane is a source similar to a global monopole embedded in 3 infinite
extra dimensions. Brane produces a deficit angle at infinity and may localize a
meta-stable 4D graviton. Although bulk cosmological constant is zero, conserved
supercharges can not be defined on such a background.
