  Context: The Crab pulsar and its nebula are the origin of relativistic
electrons which can be observed through their synchrotron and inverse Compton
emission. The transition between synchrotron-dominated and
inverse-Compton-dominated emissions takes place at $\approx 10^9$ eV. Aims: The
short-term (weeks to months) flux variability of the synchrotron emission from
the most energetic electrons is investigated with data from ten years of
observations with the Fermi Large Area Telescope (LAT) in the energy range from
60 MeV to 600 MeV. Methods: The off-pulse light-curve has been reconstructed
from phase-resolved data. The corresponding histogram of flux measurements is
used to identify distributions of flux-states and the statistical significance
of a lower-flux component is estimated with dedicated simulations of mock
light-curves. The energy spectra for different flux states are reconstructed.
Results: We confirm the presence of flaring-states which follow a log-normal
flux distribution. Additionally, we discover a low-flux state where the flux
drops to as low as 18.4% of the intermediate-state average flux and stays there
for several weeks. The transition time is observed to be as short as 2 days.
The energy spectrum during the low-flux state resembles the extrapolation of
the inverse-Compton spectrum measured at energies beyond several GeV energy,
implying that the high-energy part of the synchrotron emission is dramatically
depressed. Conclusions: The low-flux state found here and the transition time
of at most 10 days indicate that the bulk ($>75$%) of the synchrotron emission
above $10^8$ eV originates in a compact volume with apparent angular size of
$\theta\approx0.4" t_\mathrm{var}/(5 \mathrm{d})$. We tentatively infer that
the so-called inner knot feature is the origin of the bulk of the $\gamma$-ray
emission.
