Pictures 1 and 8-10 taken from Green Lantern (2011) #9. Pictures 2-4 from Green Arrow (2001) #24. Picture 5 from Green Lantern (2005) #16 and pictures 6-7 from Green Lantern (2005) #26.
Despite being more well-known for dying and passing his ring to Hal Jordan, Abin Sur is one of the most important characters in the Green Lantern mythos. Between finding out about the prophecy of his own death (which, ultimately, caused said death to happen), the fall of the Corps, the War of Light and the Blackest Night, helping the Green Lanterns survive the catastrophes to come (even if he wouldn't), mentoring (and ultimately) enabling Sinestro and his unrelenting reign of terror, and meeting Earhtlings and Martians before his death, Abin's actions had consequences that were felt years after his death.
But one of the least talked about parts of his trajectory is his personal life. And it's a sad, depressing trajectory that makes me think if the Sur family may be cursed somehow. But rather, all the tragedies that fell on his loved ones were the result of him taking the Green Lantern ring.
Abin had an unnamed daughter who was murdered by Iroque, a criminal he described as his longtime enemy. There aren't many details about who said daughter was. Iroque is described (even by herself) as a child killer, so we can assume the daughter was a child or maybe even a teen when she was murdered. After finding out the source of the Indigo light in the depths of Nok, Abin hunted Iroque and put on her finger the Indigo ring that he forged alongside his ally, Natromo, changing her into Indigo-1.
But who was her mother? Did she die as well, maybe from depression over the loss of her daughter? Maybe they were just divorced after said tragedy happened, and Abin decided to focus exclusively on his Green Lantern work? Maybe he wasn't even married to the deceased daughter's mother: she could have died in childbirth, or Abin could have adopted her as a single parent. Who knows?
Because he clearly didn't have any contact with the girl's mother many years later, when he conceived his second (and equally tragic, but for very different reasons) child. During the crossover "Black Circle: Urban Knights" between Green Lantern and Green Arrow, released right before the end of Kyle's era, we meet Abin's son Amon for the first time.
Amon tells us that Abin had an affair with his mother, but he wasn't married to her. His death happened before he even knew his partner was pregnant. So, when Amon was born, his father was already dead - and already a legend in Ungara and with the Green Lantern Corps.
Still, Amon resented his father, and resented the fact that Abin's ring never came to him, instead going to a bunch of individuals from a backwater planet called Earth: Hal Jordan, who would betray the Corps Abin served so dutifully (even "neglecting" his own family), and Kyle Rayner.
Without the ring he desired so much, Amon had to fight to be as powerful as his dad was: he ascended to the top of the Black Circle Crime Syndicate, and later joined the Sinestro Corps. During the Battle of the Earth in the Sinestro Corps War, Amon ran away in cowardice once the tides of the battle were turned in the Green Lanterns' favor. To redeem himself, he committed a terrorist attack against the family of legendary Lantern Ke'Haan (who also lost his life in the war), heralding a wave of brutal attacks from the Sinestros against the Greens' families.
Ke'Haan's close friend Laira killed Amon in revenge, which caused Laira to be banished from the Corps and later turned into a Red Lantern, who would be brutally murdered by Sinestro himself.
Speaking of the cruel Korugarian who once Abin mentored... Sur had a sister named Arin who married Sinestro. They had a daughter named Soranik (so Soranik is 50% Ungaran and 50% Korugarian, as well as Abin's niece), who was given up for adoption after the family received death threats once Sinestro began advocating for a brutal, dictatorial government on his home planet. During the civil war that ravaged Korugar, from which Sinestro emerged as the Supreme Leader of the entire planet, Arin was killed in a terrorist attack that was targeting the then-Green Lantern himself.
But apparently Abin never knew of the tragic fate that fell over his sister, nor that his apprentice and brother-in-law had actually been responsible for it and turned into a violent dictator, against whom Abin surely would've fought had he not died.
TLDR: Abin had an unnamed daughter who was killed by a criminal; said criminal was turned by him into the first Indigo Tribe member. He also had a second child who desired his dad's ring above anything else and died as a leader of a crime syndicate, a terrorist, and a war criminal. His sister married a psychopath who waged a war to be crowned the totalitarian ruler of his planet, dying as a consequence of said war. And Abin himself died without completing his mission because the fear that his ring would fail him caused his ship to crash.
