The children of your bereavement (born during your captivity) shall yet say in your ears, the place is too narrow for me; make room for me that I may live. Amp.
Isaiah 49 is promising Israel that after their captivity in Babylon that they will again be fruitful coming out on top with a mighty offspring. He promises them safety for their children. He promised them that He would still be with them in the strange land they were in. That He had a plan for them. He was always trying to encourage them, even when they were being punished.
I think that some hang on to their sins because the Lord does not deal harshly with them. His mercy overtakes His judgment at the end and restores to them what they had lost and more. All will know that He is their Savior.
He had a plan for their punishment, and a plan for their deliverance. They were to be a witness to the other nations of the Mighty God who judged them. He does not want only to be known as a God Who judges, but to be known as merciful and compassionate in all His ways.
At the same time, He will stand up for Israel and cause Her enemies to bow down to them, verse 23. He will raise up their land from the ruins and bless them and guide them.
He always saw the end blessing that He had waiting for them after their captivity.
Jeremiah 29:11 For I know the thoughts and plans that I have for you, says the Lord, thoughts and plans for welfare and peace, and not for evil, to give you hope in your final outcome.
Anytime He brings judgment upon His people, He is waiting patiently for them and us to learn the lesson we so desperately need to learn. When it is learned we can expect a blessed afterward just because He is so good.
Psalm 126:1 When the Lord brought back the captives who returned to Zion, we were like those who dream (it seemed so unreal). Amp.