you would assume its complete in the absence of a double period. For instance, he said "some random shit". The quote in the previous sentence is a complete one. But then he said " some other ..". An incomplete quote. I personally think we should include the full stop though as it conveys more information and is less cognitive overhead, "it's obviously not redundant.". Even considering that we tend to treat punctuation as breaking/pausing I still think its appropriate as the quote ended AND its containing sentence.
>you would assume its complete in the absence of a double period
That is true for the inner sentence, but again, I'm talking about the outer sentence. It needs its own terminator to make it unambiguously clear that it is complete.