Council tax reduction

Hello, I am so confused and hoping to get some more helpful advice!

I am a carer for my husband and get carers allowance and element as well as being on UC as a joint claim but am looking at setting up a small business to bring in some extra money.

I am aware of the maximum I can earn is to keep both but if I came off them due to potentially earning more than the allowed rate, would we lose our council tax reduction ? I cannot remember why we got it!! My husband is on ESA, LCWRA as well as enhanced pip for both components .

Thanks !