What you could say is that within a single cell at a single point in time fat can only be in the process of being synthesized/stored or broken down/released.
What the aggregate body does in terms of energy balance over time is harder to tell.
For example, you could overwhelmingly be in “storage” mode (insulin above baseline), yet still be losing fat, as Professor twinkie diet reminds us. If only a single cell burns fat and no new fat is concurrently incoming or being synthesized off of carbohydrates, you are effectively in negative energy balance a.k.a. “fat loss mode”.
Conversely, you can be in the deepest purest depths of ketosis, very much a catabolic state, yet still be gaining fat because of your cells feeding on that last buttery steak you had an hour ago as opposed to your native abdominal fat. Technically you wouldn’t be storing the excess right then and there but neither would you be burning it; it would just float around the bloodstream unproductively, waiting for the next opportune moment for either storage or consumption.