One of the purposes of ridge regression is to curb the effects of outliers which may cause the regression coefficients to be so large and hence cause a highly biased model.
That's why the constraint $\Sigma\beta_j^2<s$ is imposed, forcing the coefficients to not exceed a certain value.
Here is my issue. An outlier could be a value that is either too large or too small. I think this should mean than outliers could cause the $\beta_j$'s to be too small or too large. The formulation of this constraint inequality seems to only care about controlling those outliers which might make the $\beta_j$'s too large.
I believe Ordinary Least Squares Regression equally suffers from the effects of very small outliers.
Can someone please explain if or how Ridge regression controls the "small" outliers as well?