The Prophet ﷺ used to pray eleven rakʿat in the late part of the night, and when dawn appeared, he would offer two rakʿat and then lie on his right side till the Muadhdhin came to inform him (that the morning prayer was due).  

عَنْ عَائِشَةَ ؓ كَانَ النَّبِيُّ ﷺ يُصَلِّي مِنَ اللَّيْلِ إِحْدَى عَشْرَةَ رَكْعَةً فَإِذَا طَلَعَ الْفَجْرُ صَلَّى رَكْعَتَيْنِ خَفِيفَتَيْنِ ثُمَّ اضْطَجَعَ عَلَى شِقِّهِ الأَيْمَنِ حَتَّى يَجِيءَ الْمُؤَذِّنُ فَيُؤْذِنَهُ