When foreign words or proper names are used in Japanese, some modifications are necessary, in particular a lot of vowels are introduced. E.g. 'plastic' (two syllables) becomes プラスチック (five). In this case, it is not that the three /u/ will turn out to be unvoiced: this vowel was chosen precisely to yield a pronunciation not too different from 'plastic' -- it is unvoiced by design so to speak.
So are there either formal rules or a tendency to silence these vowels to be as close as possible to the original? Or is there no special status?