She's pocketing the fiber of the food and sucking out the juice or fat of the food. Very common for kids who either can't manage the fiber OR kids who are on a nuggett/kd diet who are used to high fat, high salt, melt in your mouth... slide easily down foods. I solve this by pureeing the food down to the consistency of clam chowder. I make combo stews of meat, veg, beans, rice, broth, and run them thru the processor and serve. My kids LOVE it. I also slow cook then puree down fruits to the consistency of thick applesauce.

She won't be able to pocket puree.

Once she accepts this then gradually you can increase the consistency by throwing in bits that are chewable or making the puree thicker and less blended. You can also throw in extra new flavors of veg and meat they aren't used to so gradually they become accostomed to the new taste.