Here is a list of people whose cats are spayed.
Here is a list of people whose cat is spayed.
If every person has one cat, which sentence is correct? Or are both correct?
And does this sentence deal with distributive plurals?
If each person has just one cat, then both are correct; if some of the people have more than one, then only the first is correct. In the first sentence, cats is an example of what Quirk at al (1985.768) call the 'distributive plural'. They would use the term 'distributive singular for cat in the second example.
With the distributive plural, ambiguity is possible - perhaps the people in the first example have more than one cat. While the distributive plural is common in English (The men took off their hats and coats...), we prefer the distributive singular if we want to make it clear that there is only one of each item for each subject.