Cease To Desist
First, understand the wording. The correct phrase is not really cease to desist, but rather, cease and desist. We know what you mean, but when it comes to the legal status of things, we want to make sure we get it right.
Second, understand the cease to desist degrees. You want someone, presumably who is trying to collect money, to stop that activity. It becomes a matter of degrees. There is a full cease and desist or a limited cease and desist. There is also applicability. If you owe unsecured debt, such as a credit card to ABC Bank, because you have an ABC Bank issued credit card, then ABC Bank has the right to collect their money. Whey you signed the credit card agreement, you gave them the permissions to write or call or email you in order to get the money they are due. In such a case, there is no cease to desist situation that works. They are allowed by law to contact you.
If, however, they get tired of waiting, and either hire a collection agency or sell the debt to a junk debt collector, you have different options. You can do a full cease to desist, but what purpose would it serve? The cease and desist would prevent them from contacting you, but it, by itself, does not make the debt go away. What is their only other option? Take you to court. It is almost an invitation to a lawsuit.
The other cease to desist option is a limited cease and desist letter. This would stop the phone calls, but it allows them to contact you through the mail. It leaves open a line of communication by which you can receive potential settlement plans from them.
So you ask, why would I only use a limited cease to desist? Think of it from their point of view. What is their job? It is to collect the money that you owe. If you tell them they can't contact you at all, they will find someone who can. that would be the local sheriff of processor who hands you the summons to appear in court. If you tell them you can not take phone calls, but you still want to work it out, would they send something in the mail, you have left them options. Now they can get you the payment information they want, and you can call them with your response at your convenience.
Realize that most bill collectors have a job to do - get the money. They will find a way to do their job. Most of them would rather work with you to negotiate a settlement plan. To cut them off with a full cease to desist not only keeps you from receiving the settlement offer, but makes them angry at the added aggravation. Whereas once they might have been willing to work with you, the cease to desist has taken away that motivation.
Cease to desist or cease and desist, it's the same. It's worth considering, but choose wisely what you intend to do.