Narrated Ibn 'Abbas:
If a man falls ill during Ramadan and he dies, while he could not keep the fast, food will be provided (for the poor men) on his behalf ; there is no atonement (for his fasts) due from him. If there is some vow which he could not fulfill, his heir must atone on his behalf.

حَدَّثَنَا مُحَمَّدُ بْنُ كَثِيرٍ، أَخْبَرَنَا سُفْيَانُ، عَنْ أَبِي حَصِينٍ، عَنْ سَعِيدِ بْنِ جُبَيْرٍ، عَنِ ابْنِ عَبَّاسٍ، قَالَ إِذَا مَرِضَ الرَّجُلُ فِي رَمَضَانَ ثُمَّ مَاتَ وَلَمْ يَصُمْ أُطْعِمَ عَنْهُ وَلَمْ يَكُنْ عَلَيْهِ قَضَاءٌ وَإِنْ كَانَ عَلَيْهِ نَذْرٌ قَضَى عَنْهُ وَلِيُّهُ .