Op-amp circuit voltages after power off
The input stage (for each input) will look something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

D1 and D2 are clamping diodes, and cannot handle more than 5mA continuous (a fairly typical situation), so what matters is self-heating in these diodes. These are standard silicon diodes in this instance (the 0.7V rating gives it away).

This is sometimes listed as the maximum pin injection current, incidentally.

It really is not at all unusual to see external clamp diodes (use Schottky devices) on input to prevent the amplifier input voltages achieving a voltage so that the internal clamps do not turn on when it is not practical to use series resistors.