Fell from a mulberry tree this morning–09/22/2010 Unusual color (reddish purple), about1-3/4″ long. (Lead Hill AR USA)
Your caterpillar will become the White-blotched Heterocampa moth.
This insect is found in eastern North America south to TX.
The caterpillars are found in areas where oaks grow as they feed on oaks…do you have an oak tree near the mulberry?
Since your caterpillar is so pink and with faint markings, it means it is ready to pupate. That is probably why it dropped. It will pupate for the winter then the adult moth will emerge in Spring.