After leaving Arafah the pilgrim goes to Muzdalifah, prays Maghrib and Isha combined, stays the night, and makes dhikr and du'a at the Sacred Monument until after Fajr, as Allah says, "remember Allah at the Sacred Monument (al-Mash'ar al-Haram)" (2:198). The Prophet permitted the weak — women, children, and the elderly — to depart after the latter part of the night to avoid the crush; Ibn Abbas said the Prophet sent him ahead among the weak ones of his family by night. Scholars differ over whether the stay at Muzdalifah is a pillar or an obligation, but the majority hold it a wajib whose neglect requires a fidyah.
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.