Other famous cemetery inhabitants called Wednesday include Wednesday Addams of the Addams Family.
Today Wednesday the cat was taken to a vet, who said she had been de-sexed.
One of her rescuers, Rob Isaac, said Wednesday looked to be in excellent health, according to vets.
"We estimate she is 1 to 2-years-old. She has no microchip."
Since Adams' almost 700,000 Twitter followers - and many other cat lovers across the internet became engrossed in the cat rescue saga - the hashtag #cemeterycat has been trending.
If you think Wednesday might be yours, or to check out other rescue cats available through Lonely Miaow, go to the website.
To donate, go to its Givealittle page.
Ryan Adams is in New Zealand for two shows - one was last night in Auckland and another in Wellington tomorrow.
The singer-songwriter is a self-proclaimed animal lover and contributed to a compilation album that was sold in 2012 to raise funds for an abandoned kitten that needed surgery.
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