Yes, نبی کریم (صلی اللہ علیہ وسلم) explicitly granted a concession for weak and vulnerable حجاج to leave مزدلفہ after midnight, before the Fajr نماز. He permitted his wife Sawda bint Zam'ah and other members of his family who were weak to leave early and proceed to منیٰ ahead of the main body of حجاج. This was done to protect them from the crush of crowds during the mass departure at dawn.
This concession applies to: elderly حجاج, those with illness or physical weakness, women (especially those who may face difficulty in crowds), young children, and the companions or caregivers of any of these groups. The caregiver's concession is important — if an elderly person needs assistance, their helper may also leave early.
Those who depart early should proceed directly to منیٰ and perform the stoning of جمرات al-Aqabah (the largest pillar) before the main crowd arrives. This is actually a significant practical advantage, as the stoning area becomes extremely congested later in the day. The minimum time threshold for the concession is after midnight — leaving before midnight without a genuine ایمرجنسی would mean missing the wajib of the مزدلفہ stay, which requires compensation (fidyah).