This sounds like an intense emotional release triggered by a reunion. A few concepts describe this:

Overwhelm/Emotional flooding - the nervous system gets flooded when suppressed emotions (grief, longing, relief) suddenly surface all at once.

Catharsis - a deep emotional release, often involving crying, that brings temporary exhaustion or relief.

If the person actually passes out (loses consciousness), that's likely a vasovagal syncope - a fainting response triggered by extreme emotional stress. The brain briefly reduces blood flow, causing loss of consciousness.

The overall experience is sometimes called an emotional cathartic breakdown or acute stress response.

There isn't one single medical or psychological term that captures the full picture (reunion + crying + fainting), but the combination is best described as:

In literature and everyday language, people often call it "crying until she collapsed" or "overcome with emotion." In psychology, the crying-to-exhaustion pattern is sometimes called emotional exhaustion syncope when it ends in fainting.

Is there a specific context you're asking about - fiction writing, a real experience, or something else? That might help me point you to a more precise term.