I believe Jonas is alive because on page 179 it said “He forced his eyes open”, which means he would still be alive. Also The Giver said he loves Jonas, why would he send Jonas to death. I think the elsewhere is where there is music because it said on page 180 “he heard people singing”. Also why would Jonas bring Gabe if they would die? Why would he take Gabe through all that starvation and pain when Gabe could just be released?
Jonas had so much courage to get to the elsewhere why would he want to go to death. I think the end music is from a nearby community. On page 178 it said “His heat surged with hope” which means if your heart is still functioning you are alive. If you are dead you cannot hear music and Jonas heard music which means he is alive.
So I think overall Jonas is still alive because of these reasons.