I see that going through my dad is first preference and I am fourth. Is it true that through my dad she could come while her case is pending?

Our concern is our father’s health. What would happen if he petitions for her and, she comes here, but before she gets her green card, he passes away?

How old is your sister?  If she is under 21 then your father can petition for her as an immediate relative.  Otherwise, you are quite right, petitioning through your father is first preference and you are fourth preference.  Is your sister married?  If she is married, she no longer qualifies as an “Unmarried Son or Daughter of a U.S. Citizen” and becomes a “Married Son or Daughter of a U.S. Citizen.” This change in categories may result in a significant delay in her immigrant visa becoming available.

The best strategy in your sister’s case is for BOTH of you to file I-130s sponsoring her.  There is nothing that prevents joint sponsors from filing visa petitions for her and it ensures that, in the event of someone’s death, she does not lose her place in a line.

There is a huge disparity in the waiting times for first and fourth preferences.  The waiting time for first preference is about 5 years and fourth preference is about ten years.  If you sister marries, she converts to third preference and the wait is eight years. 

Also, the Family Sponsor Immigration Act does have provisions which permit a substitute sponsor to take the place of the decedent as sponsor.  The Act, however, requires a showing of hardship and it is not something that I would want to rely on in being able to substitute you for your father.