Sharp Turn in Logistic Regression

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Hi
I am trying to remember the name of the situation in logistic regression when all data points beyond a fixed one are all successes or all fails. So we have data points## ( a_{i1}, a_{i2},.., a_{in} , 0/1) ##, with data points ##a_{ij}##ordered; last input a Boolean and a fixed value for j after which all inputs are 0 or all are 1s. Informally, the logistic curve has to do a sharp turn when all Boolean values are equal beyond a certain point. Thanks.
 
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Does the term saturation apply?
 
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