Nonparametric Regression on the results of a Linear Regression

So I was recently talking to this guy who told me that he regressed some price data on some independent variables before taking those predictions and regressing the price data onto the predictions of the linear regression with a nonparametric method.

I was wondering under what circumstances it would be a good idea to do something like that?

Edit: A little clearer

Matrix of independent variables: X

Vector of dependent variable values: Y

LinearRegression.fit(X,Y)

NewPrediction = LinearRegression.predict(X)

Nonparametricmethod.fit(NewPrediction,Y)