  It remains unclear how solar flares are triggered and in what conditions they
can be eruptive with coronal mass ejections. Magnetic flux ropes (MFRs) has
been suggested as the central magnetic structure of solar eruptions, and their
ideal instabilities including mainly the kink instability (KI) and torus
instability (TI) provide important candidates for triggering mechanisms. Here
using magnetic field extrapolations from observed photospheric magnetograms, we
systematically studied the variation of coronal magnetic fields, focusing on
MFRs, through major flares including 29 eruptive and 16 confined events. We
found that nearly 90\% events possess MFR before flare and 70\% have MFR even
after flare. We calculated the controlling parameters of KI and TI, including
the MFR's maximum twist number and the decay index of its strapping field.
Using the KI and TI thresholds empirically derived from solely the pre-flare
MFRs, two distinct different regimes are shown in the variation of the MFR
controlling parameters through flares. For the events with both parameters
below their thresholds before flare, we found no systematic change of the
parameters after the flares, in either the eruptive or confined events. In
contrast, for the events with any of the two parameters exceeding their
threshold before flare (most of them are eruptive), there is systematic
decrease in the parameters to below their thresholds after flares. These
results provide a strong constraint for the values of the instability
thresholds and also stress the necessity of exploring other eruption mechanisms
in addition to the ideal instabilities.
