Behavior of AVR microcontroller only containing bootloader
Well, the answer its to the behavior of the system is "who knows" because you basically have an undefined behavior because there is nothing written to flash to the MCU will try to use whatever is at address 0 as the reset vector for the application, if is erased it will try to use 0xffff and I do not think that the AVR issues an exception when you go outside the memory bounds and it will execute some random instruction and probably hang in there until the watchdog or other invalid instruction causes a reset. Most boot loaders tend to do a check for the value at the reset vector (typically address 0) to verify it is not blank and if it is they just loop the boot loader indefinitely to prevent the MCU to run into undefined behavior.