Hello Christopher.
When you have a stack configured, you must look at the stack as a single unit. You are not configuring the master, but you are configuring the stack as a whole. Each stack has only one configuration file, which is distributed to each member in the stack. This allows each switch in the stack to share the same network topology, MAC address, routing information, VLAN configurations… everything. In addition, this allows for any member to become the master, if the master ever fails.
If one switch is lost due to power, the rest of the switches will continue to function. However, the end devices served by the switch that lost power will no longer function. However, starting from the 3750 series onwards, the stacking technology includes what’s called StackPower, which provides power through the stack from one switch to another if a power supply fails, or if a switch is accidently unplugged.
As for how many switches must go down before you lose the stack, that depends on what you mean by “lose the stack”. If power goes off on some switches, the end devices on those switches will no longer be connected. Also, if the switches with the uplinks to the distribution layer go down, connectivity to the distribution layer will be interrupted. Also, if two switches lose power and they are not adjacent to each other on the stack, then the stack will split into two autonomous stacks. All of the above create some level of malfunction on the network, however, individual switches which still have power will continue to function even if all other switches have gone offline.
I hope this has been helpful!
Laz