  Numerical and observational evidence suggests that massive white dwarfs
dominate the innermost regions of core-collapsed globular clusters by both
number and total mass. Using NGC 6397 as a test case, we constrain the features
of white dwarf populations in core-collapsed clusters, both at present day and
throughout their lifetimes. The dynamics of these white dwarf subsystems have a
number of astrophysical implications. We demonstrate that the collapse of
globular cluster cores is ultimately halted by the dynamical burning of white
dwarf binaries. We predict core-collapsed clusters in the local universe yield
a white dwarf merger rate of $\mathcal{O}(10\rm{)\,Gpc}^{-3}\,\rm{yr}^{-1}$,
roughly $0.1-1\%$ of the observed Type Ia supernova rate. We show that prior to
merger, inspiraling white dwarf binaries will be observable as gravitational
wave sources at milli- and decihertz frequencies. Over $90\%$ of these mergers
have a total mass greater than the Chandrasekhar limit. If the merger/collision
remnants are not destroyed completely in an explosive transient, we argue the
remnants may be observed in core-collapsed clusters as either young massive
white dwarfs offset from the standard white dwarf cooling sequence or as young
pulsars (in the event of neutron star formation through accretion-induced
collapse). Finally, we show collisions between white dwarfs and main sequence
stars, which may be detectable as bright transients, occur at a rate of
$\mathcal{O}(100\rm{)\,Gpc}^{-3}\,\rm{yr}^{-1}$ in core-collapsed clusters.
