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"He shut the party down" can easily be changed into "he shut down the party". There's no change in meaning here. "The students were told to shut up" I think is a good example of a non-separable verbal phrase.

What exactly do you want? you can find native English speakers here

Another example I just thought of " shut down/up" 1. He shut the party down. 2. He was asked to shut down the party. 1. The students were told to shut up. 2. The teacher was told to shut the students up. Only some verbs can do this... hmm..

TBH, I think most teachers here do not have students who are at your level and ask such difficult questions like that one from yesterday. Hahaha xD