Sad for the news but... the show must go on. Ask Audra McDonald, back in 2007 she only missed the Saturday matinee to attend her father's funeral but was back at 110 IN THE SHADE for the 8pm performance. That's not entirely accurate, in this case. Several performances (I believe three in total) were cancelled when Audra's father died, to allow her to travel to California, attend the funeral, and travel back to New York.
It's different for everyone. Some people will choose to perform. My dear friend was Ruth Gordon's assistant for many years, and told me that Gordon never missed a performance for any reason. This included missing several family funerals. Others will take the time off. I think what's a general rule though, like with any other job, is that people who do take a personal day will try to get back to work as soon as possible.
My condolences to Judy and her family.
"You travel alone because other people are only there to remind you how much that hook hurts that we all bit down on. Wait for that one day we can bite free and get back out there in space where we belong, sail back over water, over skies, into space, the hook finally out of our mouths and we wander back out there in space spawning to other planets never to return hurrah to earth and we'll look back and can't even see these lives here anymore. Only the taste of blood to remind us we ever existed. The earth is small. We're gone. We're dead. We're safe."
-John Guare, Landscape of the Body