Citizens of some countries, such as India, automatically lose their citizenship when they naturalise as a citizen of another country. However, this has to be acknowledged, so Indians have to apply to surrender their citizenship and have their passports canceled. Some countries require you to inform them even if you don't lose their citizenship, and some require you to inform them in order to retain citizenship upon naturalisation in another country (sometimes before, and sometimes after). There are many scenarios. The US does not inform the country of your former/other citizenship when you become a US citizen, so if it's anyone's responsibility to do it, it is the citizen's.