|Tray haven wrapped around a high chair|
Tray Haven is a new product that deals with this problem. I don't think this will work with a toddler who is used to more freedom to move around, but it can be a huge help with a baby who is just beginning to sit up. Tray Haven is basically a breathable mesh netting in sections which can clip behind a high chair or stroller and creates a see through barrier keeping food, toys and whatever else is on the tray off the floor.
It is very easy to set up and this video demonstrates just how easy it is:
Babies get frustrated too when their food and toys fall, so the Tray Haven may help keep them contented. This product may also be helpful with special needs children and adults with motor control difficulties.