I think Jonas is alive because at the end of the book Jonas and Gabriel are going down the hill, he hears music but he’s never hear if music before so he’s hearing beyond. It could not have been a memory of his, because The Giver kept the memory of music. When Jonas and Gabe were freezing cold, Jonas decided to use his memory of sun and warmth to keep Gabe and himself warm.
He doesn’t have a lot of memory left but he has just enough memory to keep going, until he gets to elsewhere which I think is another community with love , colour , and feelings. In chapter twelve Jonas has a dream of him going down the hill on the sled and it says it seemed as if there was a destination where the thickness of snow brought the sled to a stop. It was welcoming , it was happened in the last chapter , when Jonas and Gabe were going down towards the destination , that was in his dream which I think is a new community that would take care of Gabe and Himself . The place he always felt was waiting.