Do you have to cancel xbox live?

I do not know how the money should continue to debit me but well

Must be canceled, as it is a subscription.

Depends on which payment data you have specified. If you only paid for gold using prepaid cards, the subscription can't be renewed at all if you do not buy new prepaid cards.
However, if you have specified a bank account, then it could well be that the subscription continues, depending on what you have set.