According to the following verses, if someone is ill or traveling and cannot fast, they can make up an equal number of other days for the days that they missed. Alternatively, if someone can fast but fails to complete the fast they can feed a poor person for each day they are not able to complete.
This means that they attempt to fast to the best of their ability but can resort to feeding a person for the days they are not able to fulfill. I believe this is reaffirmed by the statement that “fasting is best for you.” This is because even if we are not able to complete the full duration of the fast, it is still best for us.
[2:184] Specific days (are designated for fasting); if one is ill or traveling, an equal number of other days may be substituted. Those who can fast, but with great difficulty, may substitute feeding one poor person for each day of breaking the fast. If one volunteers (more righteous works), it is better. But fasting is the best for you, if you only knew.
أَيَّامًا مَعْدُودَاتٍ فَمَنْ كَانَ مِنْكُمْ مَرِيضًا أَوْ عَلَىٰ سَفَرٍ فَعِدَّةٌ مِنْ أَيَّامٍ أُخَرَ وَعَلَى الَّذِينَ يُطِيقُونَهُ فِدْيَةٌ طَعَامُ مِسْكِينٍ فَمَنْ تَطَوَّعَ خَيْرًا فَهُوَ خَيْرٌ لَهُ وَأَنْ تَصُومُوا خَيْرٌ لَكُمْ إِنْ كُنْتُمْ تَعْلَمُونَ
[2:185] Ramadan is the month during which the Quran was revealed, providing guidance for the people, clear teachings, and the statute book. Those of you who witness this month shall fast therein. Those who are ill or traveling may substitute the same number of other days. GOD wishes for you convenience, not hardship, that you may fulfill your obligations, and to glorify GOD for guiding you, and to express your appreciation.
شَهْرُ رَمَضَانَ الَّذِي أُنْزِلَ فِيهِ الْقُرْآنُ هُدًى لِلنَّاسِ وَبَيِّنَاتٍ مِنَ الْهُدَىٰ وَالْفُرْقَانِ فَمَنْ شَهِدَ مِنْكُمُ الشَّهْرَ فَلْيَصُمْهُ وَمَنْ كَانَ مَرِيضًا أَوْ عَلَىٰ سَفَرٍ فَعِدَّةٌ مِنْ أَيَّامٍ أُخَرَ يُرِيدُ اللَّهُ بِكُمُ الْيُسْرَ وَلَا يُرِيدُ بِكُمُ الْعُسْرَ وَلِتُكْمِلُوا الْعِدَّةَ وَلِتُكَبِّرُوا اللَّهَ عَلَىٰ مَا هَدَاكُمْ وَلَعَلَّكُمْ تَشْكُرُونَ
This interpretation is confirmed in the translation where it states, “for each day of breaking the fast.” Despite this not being in the word-by-word translation it is insinuated that the person will attempt to fast through the word “yuṭīqūnahu” ( يُطِيقُونَهُ ).