This is working as intended - the effect is being applied to the opponents *current* Base Attack. Essentially when you are exhausted, your Base Attack is set to 1 for one slot. When you a play a card to further lower it, the effect will not apply since Base Attack can never be lower than 1.

But its not their current base attack. If you mouseover, it states their base attack. Then it says -X Exhaust. Then it says, total attack. So no, that is not their base attack.

Total Attack also includes any equipped weapons (or other attack increases), not just Base Attack. Easy way to test this is to equip a weapon and then become exhausted. Using this mouseover as an example where Exhaust was applied *after* equipping a weapon:

http://imgur.com/el9TOw9

In this example, Base Attack is 10. Exhaust subtracts 9. The equipped weapon gives 3 attack (a value that's independant of Base Attack). As far as the game is concerned, for that slot your Base Attack is considered to be 1:

https://imgur.com/W6lZqT6

When it comes to applying the effect of Stagger (or any other Base Attack reducing card), the game will check and see that the opponent already has a value of 1. Since Base Attack can never go below 1, any attempt to lower it further will fail - even if their Total Attack > 1.

Hello, the above post is correct in the way that Stagger works in this situation. It is the mechanic at play as intended. Incidently I've seen people get Exhauted and go into Relicym's Balm :). If you feed that exhaust shouldn't work in this way then thats a separate feedback point and you're welcome to raise as a general discussion to get feedback from others and we'll have a read too!

Honestly, both situations I would argue against, but it is a cool thing to know. I couldn't figure a useful way of using that card until you stated the above. It just made no sense to me that it would function that way.