If you are Dominican or a legal resident then the telephone company, the cable company, the water company, hotels, the banks you use, the money changers, and more have your cedula number. It is already out there if you do any business with the above.
I know of a story where some workers feared leaving their ID at our guard gate to gain access to our development. They fail to realize how many places already have their cedula number. It is already out there.
The concept is that you present your cedula to prove who you are as the national ID card. It has your picture on it. The new cedula version from this year onward is very hard to reproduce. But I suppose anything is possible.
For those without a cedula, such as visitors, a passport is often used instead of a cedula.