The serial Tx pin is actively pulled high. If you connect the Tx pin on a powered Arduino to the Rx pin on an unpowered Arduino, the unpowered Arduino will light up the “on” LED. It is a good idea to isolate your powered Tx lines with a diode, with the cathode connected to Tx. This allows the Tx pin to pull the serial line low and to transmit, but prevents it from supplying power over the serial line.
I believe you will also need a pullup resistor for the Rx pin.