It appears that Pippa passed most of the foam. I think she chewed it up into pretty small pieces when she ate it. She's been eating fine and drinking lots of water. She's had numerous bowel movements today, more than normal, so I'm thinking her body wants to get rid of that stuff. I'm taking her back to the vet tomorrow to make sure that she passed all of it. There didn't seem to be an obstruction anywhere from it, and she never vomited.
Our vets are a husband and wife team, and they both emailed me and called me several times today to make sure Pippa was doing okay. They are a blessing!
Thanks to everyone for your advice and concern. I think Pippa just gave me 50 white hairs from this experience!