Ah the 'joys' of Facebook.
I think it is nothing less than childish behaviour to set out to 'blank' somebody. but then, a lot of FB behaviour falls into that category, so I am more and more inclined to have nothing to do with it.
In 'real life' this is beyond my experience. I think it would trouble me because I find conflict difficult and would want to 'fix' whatever the perceived problem was. It would not be about winning a point for me, but I guess for some it may be.
I think it very sad when families have irreparable rifts that result in silence.
I think it is somehow emotionally deficient to retreat to silence - unless you have been very hurt and have learned by experience that the situation would not change by trying to re-engage.