I've been told during my Japanese classes, and I've also observed in anime and Japanese dramas & movies, that sometimes when talking Japanese people tend to stop halfway and omit the end of sentence especially when the sentence has some negative connotation (e.g refusal etc). For example:
Suzuki: kore wo motto yasuku shimasen ka nee.
Tanaka: sore ha chotto ..
Suzuki: buraun-san no nihongo ha naka naka jouzu desu nee.
Brown: iya, watashi ha mada mada ..
So is there a cultural reason for this behavior? What is term for it? And how should non-Japanese interpret or react if our questions or invitations are replied with such responses?
Meta note: I notice myself that the last question is a bit subjective. Should we or should we not allow this kind of subjective questions in Japanese SE?