Caution: Translations of Quran and Ḥadīth may lead to possible misapplications and misinterpretations. This site is intended for students of sacred knowledge that are proficient in comprehending classical Arabic and have a strong foundation in Islamic sciences. Also note that religious injunctions rely on several aspects beyond what one may glean through reading individual aḥādīth.
abudawud:2401Muḥammad b. Kathīr > Sufyān > Abū Ḥaṣīn > Saʿīd b. Jubayr > Ibn ʿAbbās

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.  

أبو داود:٢٤٠١حَدَّثَنَا 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