What are the types of damage can a voltage sag cause?
While technically not "electronic devices", motors are generally affected the worst.  

Motors whose speed is determined by the mains frequency (both asynchronous and synchronous AC motors) will not slow down significantly.
Instead, a higher current will be drawn to "compensate" for the decreased voltage, possibly in excess of the rated maximum. Brownout conditions can thus cause motor windings to drastically overheat, since resistive heating is proportional to the square of the current.  

Commutated motors like universal motors and DC motors running on rectified mains will slow down proportionally to the voltage. They will generally not get damaged, unless the load somehow increases at lower speed or cooling is impaired.  

Variable frequency drives will normally protect the motors and either shut down or reduce the speed in response.  

It's rare for electronics to not have undervoltage protection these days, and even when they don't they are unlikely to suffer damage.