A very limited range of scenarios. Like (in the dating or social context) when the other party has already crossed some important line in some fashion (e.g. by acting outright abusively).

In the vast majority of cases, it's really much better all around to at least try to close the loop properly and decently -- even if it runs the risk of some "cost" to yourself (which in most cases - such as having someone argue with you - really is quite trivial).