  A heterostructure composed of two parallel homogeneous layers is studied in
the limit as their widths $l_1$ and $l_2$, and the distance between them $r$
shrinks to zero simultaneously. The problem is investigated in one dimension
and the squeezing potential in the Schr\"{o}dinger equation is given by the
strengths $V_1$ and $V_2$ depending on the layer thickness. A whole class of
functions $V_1(l_1)$ and $V_2(l_2)$ is specified by certain limit
characteristics as $l_1$ and $l_2$ tend to zero. The squeezing limit of the
scattering data $a(k)$ and $b(k)$ derived for the finite system is shown to
exist only if some conditions on the system parameters $V_j$, $l_j$, $j=1,2$,
and $r$ take place. These conditions appear as a result of an appropriate
cancellation of divergences. Two ways of this cancellation are carried out and
the corresponding two resonance sets in the system parameter space are derived.
On one of these sets, the existence of non-trivial bound states is proven in
the squeezing limit, including the particular example of the squeezed potential
in the form of the derivative of Dirac's delta function, contrary to the
widespread opinion on the non-existence of bound states in $\delta'$-like
systems. The scenario how a single bound state survives in the squeezed system
from a finite number of bound states in the finite system is described in
detail.
