Ignoring someone is a manipulatory technique used at times. Ignoring the attacks of someone else through emotional detachment has a very strong effect on the attacker.
Is there a name for this kind of manipulative behavior?
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Ignoring is a type of social rejection see extracts from wiki:
Social rejection occurs when an individual is deliberately excluded from a social relationship or social interaction. ... rejection can be either active, by bullying, teasing, or ridiculing, or passive, by ignoring a person, or giving the "silent treatment."
Researchers have also investigated how the brain responds to social rejection. One study found that the dorsal anterior cingulate cortex is active when people are experiencing both physical pain and "social pain," in response to social rejection.