It is permissible for the Muhrim to stipulate a condition for exiting Ihram because of sickness and the like Sahih Muslim 1207 c
Arabic hadith text
وَحَدَّثَنَا عَبْدُ بْنُ حُمَيْدٍ، أَخْبَرَنَا عَبْدُ الرَّزَّاقِ، أَخْبَرَنَا مَعْمَرٌ، عَنْ هِشَامِ بْنِ عُرْوَةَ، عَنْ أَبِيهِ، عَنْ عَائِشَةَ، - رضى الله عنها - مِثْلَهُ
Translation
This hadith has been reported on the authority of A'isha through another chain of transmitters.