  A finite volume symplectic manifold is said to have "packing stability" if
the only obstruction to symplectically embedding sufficiently small balls is
the volume obstruction. Packing stability has been shown in a variety of cases
and it has been conjectured that it always holds. We give counterexamples to
this conjecture; in fact, we give examples that cannot be fully packed by any
domain with smooth boundary nor by any convex domain. The examples are
symplectomorphic to open and bounded domains in $\mathbb{R}^4$, with the
diffeomorphism type of a disc.
  The obstruction to packing stability is closely tied to another old question,
which asks to what extent an open symplectic manifold has a well-defined
boundary; it follows from our results that many examples cannot be
symplectomorphic to the interior of a compact symplectic manifold with smooth
boundary. Our results can be quantified in terms of the volume decay near the
boundary, and we produce, for example, smooth toric domains that are only
symplectomorphic to the interior of a compact domain if the boundary of this
domain has inner Minkowski dimension arbitrarily close to $4$.
  The growth rate of the subleading asymptotics of the ECH spectrum plays a key
role in our arguments. We prove a very general "fractal Weyl law", relating
this growth rate to the Minkowski dimension; this formula is potentially of
independent interest.
