I take it off of the foil and put it on a cutting board to pull. I then take all of the juices and fat and put it in a saucepan and add more rub, some commercial BBQ sauce, some chile pepper extract (very little since I have some with millions of scoville units), ketchup, vinegar, apple juice, more ground pepper, cumin and whatever else I feel like adding and I reduce it several times. I add a litle more ketchup, vinegar and BBQ sauce each time (sometimes some water and chicken stock) and I taste it and adjust the seasonings (more sea salt here, maybe a touch of Vietnamese fish sauce there, a little chicken stock maybe). After it's nicely reduced to a fairly thick consistency, I pour it into an ice cube mold and freeze it. Sometimes the last reduction is done in a slow oven in a small roasting pan. When it's finished freezing, I knock it into a plastic bag for storage in the freezer. Because of the fat content, it never freezes quite solid, but that's all right.
I then use it in future foil wraps right out of the bag. It really adds a nice hit of flavor and helps with the moistness. I also use it to create a finishing sauce by cutting a little of it with vinegar. So yes, some of the fat gets back into the meat, but it's not a huge amount.