  We show that a quantum system with nonlocal interaction can have bound states
of unusual type -- Isolated States (IS). IS is a bound state that is not in
correspondence with the $S$-matrix pole. IS can have a positive as well as a
negative energy and can be treated as a generalization of the bound states
embedded in continuum on the case of discrete spectrum states. The formation of
IS in the spectrum of a quantum system is studied using a simple rank--2
separable potential with harmonic oscillator form factors. Some physical
applications are discussed, in particular, we propose a separable $NN$
potential supporting IS that describes the deuteron binding energy and the
s-wave triplet and singlet scattering phase shifts. We use this potential to
examine the so-called problem of the three-body bound state collapse discussed
in literature. We show that the variation of the two-body IS energy causes
drastic changes of the binding energy and of the spectrum of excited states of
the three-nucleon system.
