I had the same problem losing a greenie with Lilly. Wanna know where I found it? Stuck to the roof of her mouth.
Yep, it had gotten all soggy and clumped up in a big glob and was practically glued to the roof of her mouth wedged between her teeth. I looked and looked for it for probably 20 mins, then finally I noticed Lilly pawing at her mouth and looking really odd. I picked her up to look at her just on instinct and could instantly tell something was very wrong. I pried her jaws open and had to dig it out with the flat end of a spoon. It was awful. Be very careful with the greenies.