Cummins returned to Sydney immediately after the second defeat in India last Sunday, and on Thursday night made the decision to remain in Australia.
Batter Travis Head said the rest of the Australian team only wished Cummins and his family the best.
"It's a hard period for him and he's got the full support of all of us - he's got a lot of close friends here," Head said on Saturday.
"The limited conversations that we've all had probably with him, it's always a hard moment.
"We fully expect him to be at home. Life's a bigger thing than cricket.
"It's more important for him to be at home than be here.
"We truck on and find ways as a team to support him and to get on with the job."
Cummins intends to return for the fourth and final Test in Ahmedabad, starting on March 9.
But his availability for that match will depend on his family situation.
Former star fast bowler Jason Gillespie, who was part of Australia's successful 2004 tour to India, said Cummins should sit out the rest of the series.
India have an unbeatable 2-0 series lead and will retain the Border-Gavaskar trophy even if Australia win the remaining two Tests.
"If I was in charge, I'd probably just say to him, 'stay at home'," Gillespie told ABC Radio.
"With all due respect, the series is gone, we can't win this series … moving forward, it might just be a really good opportunity for Pat Cummins to spend important time, precious time, with close family and friends.
"What's more important, spending time with your close family and friends and particularly your mum who's gravely ill, or the fourth Test of a series that you've already lost?
"Be a son. Be a brother, just be around your family. Family is the number one thing."
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