Parents cannot renounce U.S. citizenship on behalf of their minor children. Before an oath of renunciation will be administered under Section 349(a)(5) of the INA, a person under the age of eighteen must convince a U.S. diplomatic or consular officer that he/she fully understands the nature and consequences of the oath of renunciation, is not subject to duress or undue influence, and is voluntarily seeking to renounce his/her U.S. citizenship.
-- http://travel.state.gov/law/citizenship/citizenship_776.html
And what happens when such a minor child reaches the age of eighteen, does nothing to affirm US citizenship, attends university in the United States on foreign aid, and travels on a foreign passport, from a nation that did not permit dual citizenship?