The 63-year-old singer was told she had the disease in 2015 and admitted it was tough to "wrap [her] head around [her] own mortality" but she made two requests of her husband if she should pass away with him.
Rita - who has been cancer free for five years - said: "I wanted to have these very serious discussion with my husband and I said to him, 'Look, if something happens and I should go before you, then I just want you to know that there's a couple of things that I want. One is that I want you to be super sad for a really long time ... like, I will haunt you.' "
And Rita also urged the 'Philadelphia' actor to celebrate her life with a party.
She added: "The second was that I wanted a party. I wanted to have a celebration, and I wanted to have a lot of singing and dancing and people telling stories, and to feel like that was being celebrated."
The 'A Simple Wedding' star admitted one of the things that attracted her to her 63-year-old husband - with whom she has sons Chet, 29, and Truman, 24 - was his talkative nature.
Speaking on an episode of 'The Kelly Clarkson Show' which was recorded before she and Tom contracted coronavirus, she said: "It was one of the things, when we met, that we just got along instantly.
"First of all, I love a good storyteller. So anybody who could tell a good story, I'm down with that."
Rita grew up in a "very vocal" Greek household so liked the fact Tom - who also has Colin, 41, and Elizabeth ,37, from his first marriage to Samantha Lewes - was always chatting because "food and talking ... was pretty much our existence" for her family.
She said: "I love that. He makes me laugh all the time. He's a great storyteller."