Lexie had feelings for Jonah Carver, Abe's brother. Jonah also had feelings for Lexie and they kissed, but that's all. He was in medical school and became a vigilante with the nickname The Pacifier. The whole thing led to him getting kicked out of medical school and Lexie (who ended up helping him) was booted from the police force. He eventually fell for a girl named Wendy Reardon. Later, Stefano somehow arranged for Jonah to be accepted back into medical school. Jonah left Salem and was never seen again.
Like Jen67 said, Abe was already a cop when his brother Theo was killed by Richard Cates. Theo Carver The First came to Salem looking for answers into the death (murder) of his good friend, Danny Grant, who was Valerie's brother.
I really, really wish they would bring up Abe's past of shooting TWO unarmed young men and paralyzing them. An 8 year old boy named Larry (before Abe was in Salem) and much later, Brady Black.