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:
鈴木: これをもっと安くしませんかねえ。
田中: それはちょっと。。Suzuki: kore wo motto yasuku shimasen ka nee.
Tanaka: sore ha chotto ..
Another example:
鈴木: ブラウンさんの日本語はなかなか上手ですねえ。
ブラウン: いや、私はまだまだ。。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?