Always always always have BOTH parents file petitions. This way, if one parent becomes a citizen and the other doesn't, you still will get your green card faster. If one dies and the other does not, you do not have to get into absurd process of reinstating the petition with the other parent. Reinstatement can take up to two years for some crazy reason. It can be difficult to get, as well, because CIS wrongfully requires a showing of hardship for reinstatement.
Have your mom file for you as well. Good luck!Ask a similar question
If the petitioner dies the visa petition becomes invalid/void. Once that happens, you can petition for humanitarian reinstatement, which may or may not be approved. That allows another US citizen relative to assume the sponsorship of the petition. This means that your mother could possibly assume the sponsorship if your father passes. If your mother cannot file the petition, then your sister could file the petition for humanitarian reinstatement. The problem there is that you would change catergories to sibling which has an even longer wait.Ask a similar question
Generally, if the petitioner dies before approval, the petition is terminated. Where the petitioner dies after approval, on humanitarian grounds, USCIS may continue with the petition where you have a qualified relative who can take over and fufill the affidavit of support obligations as a sustitute sponsor.
Hopefully your father will live well into old age.