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[ngauger]

Bad night. We lost one of cats to thrombosis and heart failure. He was 8 years old. One minute he was fine and the next he couldn't stand or more his hind legs. My daughter who he had picked as his favorite human is devastated.

OMG!!!!!
We had that happen years ago, my daughter's cat too!!!!

Over the next few days (or weeks):
Let her know that there are people praying for her loss and we sympathize.
Depending on how old she is, think about getting her a sympathy card.  It helped a bit.
Remind her of The Rainbow Bridge.  
When you see her "missing" the cat, just say "I know".....
It shows her that you miss the kitty too......

She'll be ok after her mourning period.
And yes, you can get another cat, as soon as she's ready.
My kid took about a month to start thinking of another Furbaby.