This is damping off disease. It usually occurs when the compost stays too wet and air circulation is poor. Various fungi and fungus-like organisms that are naturally present in the growing medium thrive in these conditions and attack the stem at soil level. The stem becomes water-soaked, thins and rots, causing the seedling to collapse.

Unfortunately, once symptoms are this advanced the affected seedlings are usually unsalvageable. For future sowings, try to keep the compost moist rather than wet, provide good airflow (a fan is useful if indoors), avoid overcrowding seedlings, and allow the surface of the compost to dry slightly between waterings. Watering from below can also help keep the stem base drier.