... or why does my Attiny2313/ATmega168 board stay alive when I flip the switch?
The block diagram above illustrates the situation: if board 2 (right) is switched off and board 1 (left) is powered, a "high" signal on any input pin of board 2 will keep it awake and running. The board on the right goes off only if the TXD-to-RXD line is interrupted as well. Why so?
I initially thought the culprit were the pull-up resistors, so I disabled them all around the UART: board 2 was still up (LCD backlight on, LED lit, uC code running, ...).
They are there on every single I/O pin, so there is no way I can live without a DPST switch on both Vcc and TXD line. All other (hardware) workarounds mean more components.
Like a small forward voltage diode between 78L05 and Atmega168 that would prevent the LCD to stay up, but the uC would still run the code. Or a line driver chip in front of the ATmega168.
Let's keep things simple and physically interrupt both Vcc and TXD lines (RXD pin on board 2).