There is a fairly standard technique of removing outliers from a sample by using standard deviation. 

Specifically, the technique is - remove from the sample dataset any points that lie 1(or 2, or 3) standard deviations (the usual unbiased stdev) away from the sample's mean. Is it possible with this technique that one ends up removing all points from the dataset. Or, is there a property of sample stdev that prevents this from happening?