The man injures his finger while trying to climb out of pool. He has it wrapped up during a lot of the movie but at some point he removes the makeshift bandage and pulls his injured fingernail off with his teeth.
It’s up to interpretation but I found it very sad. They went through so much trauma, and a certain pet which you grow to love during the movie dies in a very painful way.
She does not die but she is definitely under water and unable to breathe. Day even believes her to be dead and starts grieving and crying but she wakes up.