In the case of my cats, they throw up from overeating their kibbles at
night, and it's still so dry and recently consumed that it almost looks like
they just took a teaspoon full of kibbles directly out of the bowl and
carried them half way across the floor.....All I have to do is pick them up
with a paper towel and throw them in the toilet....

If yours really stains the carpet, try that spray stuff they are currently
advertising on TV (Animal Planet, perhaps?) You just spray it on and the
stains miraculously disappear.....