Women, the elderly, children, sick hacilar, and those who are weak or have difficulty with crowds are permitted to leave Muzdelife after midnight (or after the moon sets) according to the consensus of scholars from all four schools. This is a confirmed Sunnah concession granted by Hz. Peygamber (sallallahu aleyhi ve sellem) himself. He sent the weak members of his family, including his wife Sawdah and others, ahead from Muzdelife to Mina during the latter part of the night to avoid the rush of the main body of hacilar departing at dawn.
Sheikh Ibn Baz explained that the concession is available to all who have a genuine reason for early departure, including women who want to avoid the extreme crowding, elderly hacilar, those with small children, and the sick. These hacilar may proceed directly to Mina and stone Jamrat al-Aqabah before dawn, which is permissible for them based on this concession. Strong, able-bodied men should remain at Muzdelife until after Fajr namaz, following Hz. Peygamber's own practice.
Sheikh Ibn Uthaymeen specified that the earliest permissible time for departure is the latter half of the night (after midnight), based on the narration that Hz. Peygamber sent them ahead 'at the end of the night' and the moon setting. He cautioned against departing too early — shortly after Maghrib and Isha namazs — as this would mean the haci barely stayed at Muzdelife at all. Those who take this concession should still pray Maghrib and Isha at Muzdelife before departing.