The phrase default loser I find somewhat strange (perhaps because I have not heard it before). The other two phrases are fine. But we say refuse, not reject (which is not followed by an infinitive).
In your sentence in #4 I don't think I would say a loser by default, since I associate this phrase with someone who fails to play a game. When you say that life has been good to someone, you are not normally talking about games. Instead we have expressions like He was a born loser.
So if you talked about a loser by default here, I would ask you what you meant. It means to me that someone has defaulted on a game.
I find it more natural to say the winner by default or I won by default.
It makes sense to say default winner, but I don't think that it is very common. The only place I could find it was in Merriam-Webster's Learner's Dictionary. There is no example in the corpuses (BNC, COCA), although there are a few examples in Google Books.