What happens to the late fees and interests that accrue when we stop making payments to creditors?

Yes, of course. The late fees and interest payments get added to the outstanding amount you're supposed to pay. So, never make late payments.
If you're struggling to repay the outstanding balance, try to negotiate with your creditors for an alternate payment plan or negotiate to settle your debts.

Hey pal,

Yeah, Good Nelly was right, the more you become late, the more debts you'll add in your outstanding balances.

You can do few things to solve this problem...

First - Cheer up and try to pay on time each month!!!

Additionally, you can set up payment reminders, pay on the card issuer's site, and save proof of payment. But if you somehow got an unfair late fee - call your card issuer and inform them.

If they do nothing to help you, file a complaint with the CFPB.