during the seattle grace-mercy west merger, izzy went back to work (even though she was still doing her chemo) cuz she was worried about her job. alex was worried that she wasn't ready to come back to work, so he voiced his corcerns to the chief. after one of her patients died, she was let go (since they were laying people off at the hospital). she blamed alex for losing her job, so she left him. she came back later to try to fix things with alex since she realized that he had nothing to do with her losing her job, but alex said that he loved her and she made him a better man, but because of that he knew he didn't deserve what she did to him and he couldn't be with her. she left again and later sent him divorce papers.
i heard that izzy is going to come back to give proper closure to her relationship with alex. idk, though. i loved them together :(
Izzie got Metestatic Melenoma of the skin, liver, & brain. After She realized her husband Alex told the Cheif that she wasnt ready for work yet, the cheif fired Izzie. Izzie left a note in Alex's locker that said she had left him. She cam back later in the show with a patient and was considering staying. But Alex told her it would be best for both of them if she left.