Volvie,
I don’t know about Israel, but that’s not true of the U.S. As per the Dept. of State:
Persons intending to renounce U.S. citizenship should be aware that, unless they already possess a foreign nationality, they may be rendered stateless and, thus, lack the protection of any government. They may also have difficulty traveling as they may not be entitled to a passport from any country.
http://travel.state.gov/law/citizenship/citizenship_776.html
The Wolf