Technically, by staying out of the U.S. for more than a year, they are deemed to have abandoned their green card. However, if you have proof of your father's illness and surgery (medical records, etc.) the abandonment issue can be overcome. When they return back to the U.S., they most likely will have their green cards cancelled and be placed in removal proceedings. They should deny the abandonment and request to be paroled in. Once they are before the immigration judge, they will need to prove the medical issues. Good luck.
Answered on Apr 28th, 2015 at 2:13 AM