What happens when a debtor sends a cease and desist all communication letter to a creditor?

It depends on the laws of the country you're in.

Here in the UK, a letter like that wouldn't be sent by the debtor. A cease and desist notice would be sent by a third-party organisation such as a debt management company or the citizen's advice bureau.

Once the creditor receives the notice - it is a criminal offence for them to 'harass or contact the debtor in any way'. All further communication must be made through the third-party.

The third party will then negotiate on behalf of the debtor, with the creditor(s) a reasonable repayment schedule based on the difference between the debtors income and expenditure. This will usually mean all interest payments will stop, and the debtor pays back the balance on the account(s) over an extended period of time.