She and Roman had a relationship regardless of Remi's disapproval. Kat also stated that Remi only cared about herself in an attempt to convice Roman to run away with her.
When Roman and Jane showed up at her bar, Kat's first interaction with the siblings was approaching and slapping Roman for leaving her without explanations and never returning for a year. As soon as she saw Jane, she recognized her from her previous talks with Roman about his sister.
She died when a bullet hit her lower abdomen.
Kat and Roman probably met doing business for Sandstorm and started a relationship in secret, however, the only who knew about this was Remi who didn't approve about Roman having a distraction from Phase 1. Regardless Remi's protests, Kat and Roman kept seeing each other until Roman left, probably before Phase 1 started.
They reunited again after a tattoo leads the team to Kat.