If OpAmp powered off Vcc, and Vcc is opened, no damage.
If OpAmp powered off Vcc, and Vcc is shorted to ground, possible damage from inputs being driven
from a voltage source.
If OpAmp powered off separate supply, and Vcc is opened, no damage.
If OpAmp powered off separate supply, and Vcc is shorted to ground, possible damage. Could be thermal,
or over current. Depends on protection designed into OpAmp.
You could supply a schematic to vendor FAE for analysis. You would have to include power sequencing
in the description.
Regards, Dana.