She is unfortunate enough to lose few friends she made during her stay in Chennai.
The writer is not using a few because the sentence is intended to test the knowledge of the reader.
As you seem to be aware, the use of the article a before few gives a completely different sense to the context.
She made few friends during her first year at university
implies that she did not succeed in making as many friends as might be hoped or expected. It suggests something about the circumstances of her stay or possibly her character.
She made a few friends during her first year at university
is a neutral statement of fact without any implication.