He was thinking about his family until the very end.
Until his very end, his thoughts were with his family.
ご質問ありがとうございます。
① "He was thinking about his family"＝「彼は彼の家族のことを考えていた」
"until the very end."＝「最後（の最後）まで。」
("until the end"だけでも良いのですが、「死ぬ直前まで」というニュアンスで"very"を入れています）
② "Until his very end"＝「彼の最後まで」
"his thoughts were with his family."＝「彼は家族のことを思っていた。」
ご参考に。
He was thinking about his family until the very last moment of his life.
おっしゃっている内容は、このように表現することも出来ます(*^_^*)
He was thinking about his family until the very last moment of his life.
「彼は人生の最期の最後の瞬間まで家族のことを考えていた」
last momentで「最後の瞬間」ということですが、それにveryを付けることで、「最後」ということがより強調することができます(*^_^*)
以上です。
少しでも参考になれば幸いです(*^_^*)
アメリカ合衆国 
日本 
