Q: I heard that when you're awakened, there's no one there to enjoy it, or even to claim it.
What you heard is based on the muddled thinking and false ontology that is endemic to spiritual teachings. Whether you're enjoying a simple pleasure like eating a croissant, or you're enjoying the great peace of being settled in conscious presence, it's your own aware intelligence that knows and understands the nature of the experience. In the case of the croissant, it's a sensory pleasure related to an object. In the case of peace, it's your own nature that knows itself.
In awakening, the only thing that's gone is an old misunderstanding or mindset that had hijacked your identity and warped your thoughts and feelings. Awakened people don't need to claim anything; they just say what is and what they've discovered. In the awakened and natural light of your being, you just acknowledge what is natural to you.
A confused mind perceives enlightenment as a superhuman achievement. In actual enlightenment, you see your own conscious light as natural and free. You just enjoy your being because your nature is enjoyment.