Yes, Hz. Peygamber (sallallahu aleyhi ve sellem) explicitly granted a concession for weak and vulnerable hacilar to leave Muzdelife after midnight, before the Fajr namaz. He permitted his wife Sawda bint Zam'ah and other members of his family who were weak to leave early and proceed to Mina ahead of the main body of hacilar. This was done to protect them from the crush of crowds during the mass departure at dawn.
This concession applies to: elderly hacilar, 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 Mina and perform the stoning of Cemerat 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 acil durum would mean missing the wajib of the Muzdelife stay, which requires compensation (fidyah).