Ludo Bagman was a serious gambler, and one who had got on the wrong side of the goblins so much so that they refused to side with wizards in the Second War. So you'd think that at the end of it all, either the goblins would've have caught up with him and done him in and that the wizarding community could really shield him no more. What actually happened?
Ludo was evidently discredited. The final mention of him in any of the books is his name being used as a byword for gambling incompetence.
‘But Dementors wandering into a Muggle suburb and just happening to come across a wizard?’ snorted Fudge. ‘The odds on that must be very, very long. Even Bagman wouldn’t have bet –’
Harry Potter and the Order of the Phoenix: CHAPTER EIGHT — The Hearing
It's not certain if he lost his job at the Ministry of Magic, but he wrote a "runners and riders" article for the 2014 Quidditch World Cup (published on Pottermore), suggesting that he'd turned at least semi-professional as a bookmaker and may be working for the Daily Prophet.
We don't exactly know.
The only mention of Bagman in the last three books is this bit from Bill:
“He’s feeling pretty anti-wizard at the moment,” said Bill. “He hasn’t stopped raging about the Bagman business, he reckons the Ministry did a cover-up, those goblins never got their gold from him, you know —”
We don't know how reliable Ragnok's reckoning actually is; but this shows that the whole wild goblin chase did end pretty quickly. But this is all we know about Bagman after book 4. The wiki says that he "lost both his credibility in the eyes of the wizarding world and his job at the ministry." However, although this is very probable, there's no citation for it. The short answer is that we don't know what happened to him.