When a complex organism uses something as respiration, a few things are needed:
0. The ability of the reaction to produce energy
1. A way for individual molecules of the food (sugar, oxygen in humans) to be transported
2. A way for your body to absorb individual molecules from the source into the body
3. A way for individual molecules of the waste (CO2, water in humans) to be transported
4. A way for your body to get rid of these waste molecules completely
The biggest problem is #4. If life was made of silicon instead of carbon, CO2 would turn into SiO2, a solid rock that doesn’t tend to dissolve or bond with anything, but does tend to crystallize. If such an organism existed, it would have to find a way of secreting this without coating itself in a layer of solid rock.
Regarding the original question, I suppose it is possible for an animal to get all necessary food chemicals from solids, since humans already get one, sugar. It would be much more difficult if the waste was a solid.