Quote Originally Posted by it-ogo View Post
Я надеюсь, что нас на границе не задержат.

It is called "неопределенно-личное предложение". "Задержат" has a form of past 3rd person plural, so subject "they" is implied but skipped. "I hope they won't stop us on the border." It is not mentioned specifically (not even before) who are "they".
And yes, it is a kind of passive voice. Normally, Russian academic grammar school does not call it "passive voice" since there is no passive verb in it. It calls it "неопределенно-личное предложение" as it-ogo wrote. But this structure is a functional equivalent of the passive voice. It is used to "remove" the real subject from the phrase since we do not know its name. "нас не задержат" = "we will not be detained". Although grammatically it is structured differently.