King Exiling

King Exiling, or "Exiled Kings", is a strategy where a player purposefully creates inactive timelines by repeatedly sending their kings in the past. Because playing on inactive timelines is optional, the kings on them become quickly unreachable from the present boards. If done well, there will be no king on any active timeline and the opponent will not be able to attack any of the exiled and will be forced to draw or loose.

This strategy is usually performed after an inactive softmate, to prevent the opponent from creating new timelines and bringing the exiled kings back into the game. It is unknown whether or not king exiling without an inactive softmate can be sound. It is believed that this strategy is usually unsound without inactive softmate.

Counterplay
Firstly, if your opponent exiles kings without first making a threatening inactive timeline, then you can easily make branches yourself to reactivate the ones with your opponent's kings. You should jump back to a board with at least one king so that you can attack them on that timeline as well.

Secondly, if your opponent's first inactive timeline is a softmate or hardmate but is not very close to the start of the game (T10 is too late), then you can jump back to the start (ideally with a queen). Since they needed to make 3 inactive timelines (one with the softmate and 2 with the exiled kings) then you can branch twice more without giving them the ability to make their own active branches. This allows you to play for 10 turns with an extra piece, then jump back and play for 9 turns with 2 extra pieces then jump back again and play for 8 turns with 3 extra pieces which should be enough to win the game.

Thirdly, you can try and deal with the softmate on the first inactive timeline by making a new timeline or two and using a piece from there to capture the piece giving softmate.