Once balance chasing starts, it won't stop until your balance reaches the target limit the lender set on the card, or (in some cases) it might close the account entirely after it's paid off... though I would think if they wanted to close the account, they'd do it right off the bat, and not let you use it at all.
In most cases with multiple cards with balances I'd say a snowball approach is the way to go, or the avalanche method. Both are similar, but with snowball you pay down/off the lowest balance card first, get it paid off, then move to the next higher balance card, and so forth. Avalanche is similar except you start with the highest APR% card first, and work your way down to lower APR cards. While doing this, you make minimum payments on the other cards.
I have an approach (not patent pending, but maybe I should apply... lol), for those who have many cards with balances and are being balance chased.
Start with taking the cards you KNOW are chasing you and just make the minimum payment on those. There's nothing more to lose on these cards, since they're already taking AA on them.
Next, take the cards you KNOW are NOT balance chasing you. Use the snowball or avalanche method on these to pay them off first. These are gold, you want to save them if you can. They'll help your utilization. Plus you can use one of them for everyday purchases and pay it off in full and not get hit with interest and (hopefully) not get any CLDs on it.
The goal here is to salvage any cards that haven't started with the chasing or CLDs and get your utilization down and your score up.
For the cards you aren't sure about, because you've been carrying balances on them for a while, hit those next. You could snowball one at a time, or if you can afford it, split your payments across them. If the card or cards you're paying down start balance chasing, switch to making small payments on it and move on to paying down another card. When you find another non-chaser, hit it with all you got until it's paid off. Rinse and repeat until you've paid off all the cards that aren't chasing.
Now, your scores should start looking a lot better with lower overall utilization and multiple cards with zero balances. Now you can snowball or avalanche the balance chasing cards. Don't worry too much about the resulting CLDs. The cards you paid off earlier will keep your utilization from spiking.
As your scores improve and your lenders review your profile, they may decide to stop balance chasing you or even restore your limits. Best of luck to you!
