I work for a major independent power producer (28000 MW) so I am only speaking for merchant plants here.
When the plant is operating, the power consumed within the plant is called parasitic load and is not charged back to the generator by the utility because it hasn't yet entered the grid but it reduces the amount of electricity that passes through the revenue meter exiting the plant. Every attempt is made to keep parasitic load to a minimum in order to lower the heatrate (lower heatrate means higher efficiency) of the plant and thereby increase revenue. (more power going out)
The turbine/generator is designed to trip offline for safety and equipment protection reasons when an upset is detected. If you lose a major transmission line or other powerplant on the system the powerplants currently online have to be able to pick up that load instantly and if they can't, such as in this case, they have under/over voltage and current protection relays that trip them offline. You don't want to be sending 500 or 1000 MW out that could possibly be going to a dead short in the system. If it's a small upset they can usually react fast enough to keep things going and all you see is a slight voltage drop.
Also, most merchant plants are not designed to operate as a power island. They need outside power in order to start up the unit and provide service to the plant when it is not operating which is purchased just like at your house.