  A significant accumulation of matter in solid Helium-4 observed during the
superflow events, dubbed as the giant isochoric compressibility (or the syringe
effect), is discussed within the model of dislocations with superfluid core. It
is shown that solid Helium-4 in a contact with superfluid reservoir can develop
a bistability with respect to the syringe fraction, with the threshold for the
bias by chemical potential determined by a typical free length of dislocations
with superfluid core. The main implications of this effect are: hysteresis and
strongly non-linear dynamical behavior leading to growth, proliferation and
possibly exiting from a crystal of superclimbing dislocations. Three major
channels for such dynamics are identified: i) injection and inflation of the
prismatic loops from the boundary; ii) Bardeed-Herring generation of the loops
in the bulk; iii) helical instability of the screw dislocations. It is argued
that the current experiments are likely to be well in this regime. Several
testable predictions for the time and the bias dependencies of the dynamics are
suggested
