what about a mcu that usually operates at 5V, but when unpowered there is still a serial tx signal left high on a pin?
Same as before.
In the end it comes down to how much current is running the wrong way through the MCU and for how long.
It will also depend on the input off state of the TX pin. If in the off state it goes high impedance then it will limit the current flow. If in the off state it's high impedance with a pullup active then current will feed through that pullup into the rest of the device.
For example many devices can stand over voltage on the wrong pins if you have large resistors limiting the current flow to a safe level. It's how the ebay sellers can get away with claiming 3.3v SD card shields are usable at 5v because they put 10k resistors on them that keeps the current low enough that it won't burn anything out.
If you can't maintain supply current you will find it sucking current in through your other pins depending on their configuration hence bypass caps can be critical too. It's all about different of potential.
Probably a good reason to leave things like brownout detection on albeit at a lower level.
After blowing up my first Arduino by putting voltage through it the wrong way
I tend to pay more attention to the state of the circuit I'm putting, it in particularly now that most of my projects are now on standalone circuits and not on Arduino boards.