All the schools agree all feelings must have an object related to them. This is because the aggregate of consciousness compiles both the aggregate of feeling and the aggregate of discrimination. The aggregate of discrimination perceives an object, and the aggregate of feeling experiences that object as a feeling. And the aggregate of consciousness knows these two simultaneously in a single mind.  

For the lower schools however, they believe there are truly existent objects giving rise to truly existent feelings. Again, this corresponds with our normal view. It seems as if we encounter objects and then experience them in different ways, therefore we conclude the objects give rise to the feelings. We have no sense whatsoever that the way our mind discriminates these objects determines how our aggregate of feeling experiences them. We feel as if we are a passive experiencer of objects. We encounter the object, it gives rise to a feeling. The object is what the object is, the feeling that arises is the feeling that arises, and our mind has no role in this process.

(9.99) All objects of consciousness that give rise to feelings – from visual forms to tactile objects –
Are like dreams and illusions, utterly devoid of true existence.
If the mind experiencing feelings is truly existent,
It cannot experience any feelings that arise simultaneously with it.

The Prasangikas point out that our normal way of looking at things is actually impossible. If the object is truly existent, then how do we come into contact with it since it exists independently of the person experiencing it?  If it exists independently, how can it enter into a relationship with anything else? If it can enter into a relationship with something, then it does not exist independently since being in a relationship with something else implies some degree of dependence. Likewise, if the mind experiencing feelings is truly existent, it also exists independently. If it exists independently, how can it come into relationship with an object?  If it can come into relationship with an object, then there is some dependence between the two, at which point it is no longer independent. If the aggregate of feeling existed independently, then how could it experience different feelings at different times? There would have to be some sort of dependent relationship between the objects and the feelings that arise in the aggregate of feeling to bring about the change. But if there is a dependent relationship between the objects and the feelings, then how can we say the aggregate of feeling exists independently? It is impossible for an independent thing to exist and change in dependence upon other things.  Therefore, a truly existent aggregate of feeling would not be able to feel anything at all. Or it would experience the same feeling at all times without ever changing.