Actually, "on" and "in" are prepositions that always need an object. The rules of grammar demand that you use a word like "it" after them. If you don't want to include objects in your example sentences, don't use the prepositions: A table with a lot of food. A box with only a few things. OR A table with a lot of food on it. A box with only a few things in it.

Sorry for you to be dealing with contradictory answers from two native-speaker teachers. I agree that adding "it" is also a correct option. "with" in these phrases has the same meaning as "that has". The "with" phrase defines the object. So perhaps this is the reason why it sounds good to me to lose the "it". Or perhaps it is a standard example of ellipsis, where a word is intentionally omitted without loss of meaning. Or perhaps there is a UK/US English variation in usage. Jonathan is from the USA and I am from the UK. I agree with Jonathan that we may also be able to lose the prepositions and not lose the meaning. But let's say the food is "on" one table and another table has food "below" it, adding the preposition adds important meaning. I would be interested to see if Jonathan thinks that this is an issue with any more to say about.

Not sure what michael is talking about. These both need IT at the end.

A table with a lot of food. or A table with a lot of food on it. A box with only a few things. or A box with only a few things in it. You can use any of those four expressions.

They are perfect. They are better and more native without "it".