The Lord is a Peacemaker
People going away can be hard to process. This could be any form of leaving from death to simply moving away to a place you can't visit often.
2 Thessalonians 3:16 says, "Now may the Lord of peace Himself give you peace at all times and in every way. The Lord be with you all."
Even though you may be worried or scared for a person you have to say goodbye to, the Lord will bring you peace of mind. The Lord is a peacemaker and trusting in him allows the Holy Spirit to work through you and give you the sigh of relief you need. This applies in not just people leaving but in our everyday lives. God offers us his love and care, so no matter how hard it is to say goodbye, he will offer his peace.