Psalm 34:18 — "The LORD is nigh unto them that are of a broken heart; and saveth such as be of a contrite spirit" — uses the Hebrew shabar for "broken heart." Shabar means to shatter, to smash into pieces — the same word used for breaking pottery or bones. A broken heart in Scripture is not metaphorical sadness. It is the specific condition of something that has been structurally shattered. God's proximity is specifically to the shattered person, not only to the mildly disappointed.
Isaiah 54:6 addresses someone who has been "forsaken and grieved in spirit, and a wife of youth, when thou wast refused." The specific words — forsaken, grieved, refused — speak to the vocabulary of abandonment that divorce trauma produces. God speaks directly into those specific experiences, not around them. "The LORD hath called thee as a woman forsaken" — he names where you are before he speaks about where you are going.
Commentary is from a charismatic Protestant perspective, drawing on KJV text and public-domain sources including Spurgeon, Andrew Murray, and Matthew Henry.