In a committed mindfulness practice, one finds that their emotions stabilize. They may still experience high highs, and low lows, but they return to an equilibrium quickly. Essentially, the mind becomes less immediately reactive to external situations. This doesn't mean the mind is indifferent; but rather, the mind is focused on the present moment - the "new now" - and fully available to it without distraction.
The practice of non-attachment to the emotions is challenging at first. There is something gratifying about feeling intense emotional states, even the negative ones from which it seems we all want to escape. But I think this could be analogous to desensitized taste buds that seek out excessively sugary or fatty foods. When we are not mindfully aware of our emotional states, we aren't sensitized to them. We actually miss quite a lot of what we do feel. So perhaps this desensitization creates the compulsive seeking of drama, good and bad. Just like taste buds that can no longer detect nuanced flavors, the mind can no longer tune into nuanced experience.
Why does mindfulness change this dynamic? Because through committed practice, an individual wakes up to the true nature of their non-Self. They recognize that all emotions, thoughts, beliefs and behaviors, whether functional or not, are a product of conditioning. It becomes possible to see the outward life as a series of temporary and fluctuating moments, no different than how thoughts enter and exit the mind. The individual then does not chase experiences, but allows them. The simplest moments, like taking a deep breath, can become enormously satisfying and profound. Consciousness in this way becomes a vessel; the individual is a conduit for experience, not a creator of them.
To the extent that we take ownership for what we do create in our lives, including our perceptions of reality, we will experience a distinct and unique identity as Self. I think the concept of Self is necessary to function in the physical world, but identification with it can lead to unnecessary suffering because it is spiritually insufficient. The Self is a thought, and while it may have a purpose, it does not withstand scrutiny. To avoid this realization, our society conditions the mind to reinforce the concept of Self, particularly through intense emotional experiences. This conditioning is gradually lost as an individual awakens. Instead of experiencing prolonged reactivity, triggered emotions lead to an awakening of consciousness and wisdom.
So ultimately it is not that emotions are no longer experienced; in fact, they will still arise even intensely, but it's that the mind no longer perpetuates dysfunctional emotional states for the purpose of self-gratification. The emotions themselves become an object of mindfulness in an awakened mind as our outward behaviors stabilize and are no longer controlled by them.