I read it as simply meaning "he is extremely generous". I see neither a negative nor positive suggestion, because "to a fault" is an expression of emphasis, much in the same way one could say "he's terribly generous" or "he's awfully generous". Neither of those expressions are negative despite using negative adverbs; they simply emphasise the word "generous". The danger of reading too literally. ;)

It just means that he's generous. Nothing less, nothing more.

Well it means that he is overly, excessively generous, so much that it is almost a fault or a weakness. So it is negative. If you take it as a weakness, you could use it to express your concern for someone "You are generous to a fault, you'll end up getting hurt one day" (but as you can still, it is still negative).

The answer depends on whether you think being generous is a good or bad thing. The statement is positive to me because it means that whoever that statement's about is a very generous person.

It is positive, it means that he will give anything that he can to a friend in need. While 'to a fault' does indicate that it is excessive, in practice it is said in a complimentary manner.