There is a great debate over what may have happened to Jonas and Gabe after they leave the community. The later books notwithstanding, if you look at The Giver on its own, the ending is not very clear. It is left to the reader to decide what may have happened to Jonas. Did he make it to "elsewhere," a place with colors and feelings and pain and joy? Or did he go to the other interpretation of "elsewhere," which is death? Did Jonas and Gabe survive the journey? Some people have argued that the music and lights at the end of the book are hallucinations or the last memories that Jonas holds. Other, more optimistic, readers have argued that Jonas finds another community where people are not so oppressed. I am attaching a link to a discussion thread where people have argued one way or the other. Join in the discussion, what do you think happened?

You will have to read Lowry's Gathering Blue to find that one out!  Although this book is not meant to be a sequel to The Giver, in it the author does give some information about Jonas and Gabriel, but I won't spoil your fun in finding out.... (Yes, they are thriving and doing well, but in what way?...)

By the way, there is a third related story called The Messenger, which is more closely related to the second book than to the first.  Enough material there for a nice, little read, so enjoy!

So you are asking what we think happens at the end of the book?

Well, it totally depends on whether you are an optimist or a pessimist, in my opinion.  I do not think there is anything in the text to tell us for sure what is going to happen.

If you like happy endings, you imagine him and Gabe going down the hill and finding people who will care for them.

If you're more pessimistic, you can just think that all of this is a hallucination brought about by the cold.  If that's the case, the two of them are dead.