Pet cannot get to shared/dropped food

It definitely sounds like an issue with the table's footprint or object placement blocking the routing. Some tables, especially CC or custom-sized ones, can have invisible barriers that interfere with interactions. You might try testing with a different table to see if the problem persists. Also, using "bb.moveobjects" and slightly adjusting the table or surrounding objects can sometimes fix these routing issues.

It is a very small house and there is not anywhere else to place the table. The house is a pre-existing one so it's not anything I have done or downloaded from the gallery that has made this an issue. I'd think if there is enough room for sims to do their thing and every day things go as normal with no routing issues, then really not more I can do. I mean I guess I could delete two of the chairs but I don't see the point because sharing food to the pet should work regardless. Plus I need the chairs. The problem is the small table and chairs not having much room beneath them and that is where the food lands when the sim drops it. That mechanic needs to be looked at I think so that when the sim drops the food it drops to the side of their chair instead of under the table. Just my thought from this experience in this house. 

Try testing by placing the table in a large open space, like outdoors, and see if the issue still remains. By doing this, you can test to see if the issue may be the space needed in the room. You may need to allow for more room when placing the table.