Since she is a Government employee, if she is dead her family is obliged to report her death to the Office of Personnel Management ("OPM") as well as to the Social Security Administration. You should not be receiving government checks if you are dead although it does not stop some people! If she is dead then OPM should be notified so that they can address any life insurance due her beneficiaries or estate. Note that to do any of these things there would have to be a Death Certificate, which could be issued by a Physician or Coroner of the county in which she died. Not every one supports her. With Nurses and doctors at the hospital and mortician word would get out.
I think she could spend a long time sick and her clerks would do her work, but I do not think that they could hide her death for long.
An Attorney would be better able to answer the question of whether a lawyer/litigant could question the absence of a SC Justice who missed Oral Arguments.