Restrictiveness

In English and some other language, it is very clear whether a phrase or a word is restrictive or not. For example "The dog that has rabies bit a cat". The phrase "that has rabies" tells you which dog bit the cat. "The dog, which has rabies, bit a cat" -- simply adds some further information, but is not identifying the dog. I don't know if there are specific conventions in Polish that show restrictiveness or not. I suspect that it is haphazard, and that the Polish language usually does not concern itself with it. Perhaps it is expressions like "właśnie"?