There is a nice answer, however it goes from another way around: the model gets more bias if we drop some features by setting the coefficients to zero. Thus, overfitting is not happening.
I am interested more in my large coefficients indicate the overfitting. Lets say all our coefficients are large. My intuition is that the larger coefficients get the less important are the features. However, if this is the case how are we able fit too much to the data if features are less important?