Hey guys,
So, after trying lots of advice without success I finally found the solution. Somebody said to scale up the size of the model, apply the rigify auto weighting and then scale down the model to its original size.
And the reason for that was, according to him, rigify is not very good at calculating the weight when the vertices are too close together.
And I noticed that the polys in the lacrimal caruncle of the eyes of my character are very small. So that was probably the reason.
Thank you all of you who’s helped me.