Does a relay with switchable output exist?

I need a relay that has two outputs on 12V: output A and B. It can be in three states: A, B or none. I must be able to switch between A and B from an Arduino, for example via a simple protocol (PWM?), or just first pulse is A, next pulse is B, etc... I have googled around for something like that but couldn't find it.

Does a relay as described above exist?

I am a bit confused. You first say A, B and none, then A, B, A, B,...

For the first case (A, B, none) a SPDT relay with NO to A, NC to B and the signal to COM through another relay. For the second case just one SPDT relay, A to NO, B to NC and signal to COM.

What are you switching? How often?

Two relays. Two digital pins.

Does a relay as described above exist?

No. You have to make that function using more than one relay.

PWM is not a protocol it is a way of turning an output on and off rapidly, great for dimming LEDs and controlling motor speeds but useless for relays.