Praise be to Allaah.
If a person starts an obligatory fast, such as making up a missed Ramadaan fast or offering expiation for breaking a vow (kafaarat yameen), it is not permissible for him to break the fast without a valid excuse, such as sickness or travel.
If he breaks his fast - with or without an excuse - he has to make up that day, but he does not have to offer any expiation, because expiation is only required for intercourse during the day in Ramadaan. See question no. 49750 .
If he breaks the fast with no excuse, then he has to repent to Allaah for this haraam action.
Ibn Qudaamah (4/412) said:
If a person starts an obligatory fast, such as making up a missed Ramadaan fast, or a fast that he vowed to observe, or an expiatory fast, it is not permissible for him to break the fast. There is no scholarly difference of opinion on this point, praise be to Allaah.
Al-Nawawi said in al-Majmoo' (6/383):
If a person has intercourse during a fast other than in Ramadaan, such as making up a missed fast, or a fast that he vowed to observe, etc, no expiation (kafaarah) is required. This is the view of the majority. Qutaadah said: He has to offer expiation if he broke a fast that he was observing to make up for a missed Ramadaan fast.
See al-Mughni, 4/378
Shaykh Ibn Baaz was asked in Majmoo' al-Fataawa (15/355):
I was fasting one day to make up for a missed fast, but after Zuhr prayer I felt hungry so I ate and drank deliberately, not because I had forgotten or was unaware. What is the ruling on this action of mine?
You have to complete the fast. It is not permissible to break the fast if that was an obligatory fast such as making up a missed Ramadaan fast or a fast that you vowed to observe. You also have to repent from what you did. Whoever repents to Allaah, Allaah will accept his repentance.
Shaykh Ibn Uthaymeen (may Allaah have mercy on him) was asked (20/451):
In the past I fasted to make up for what I owed, then I broke the fast deliberately. After that I made up that fast one day. I do not know whether that is sufficient or do I have to fast two consecutive months? Do I have to offer expiation? Please advise me.
If a person starts an obligatory fast, such as making up a missed Ramadaan fast or offering expiation for breaking a vow (kafaarat yameen), or expiation for shaving during Hajj if he shaved his head before exiting ihraam, or any other obligatory fast, it is not permissible for him to break the fast without a valid shar'i excuse. The same applies to anyone who starts an obligatory action - he has to complete it and it is not permissible for him to stop it unless he has a legitimate shar'i excuse that allows him to stop. This woman who started to make up a fast then broke her fast one day with no excuse and made up that day does not have to do anything else, but she has to repent and ask Allaah for forgiveness for breaking an obligatory fast with no excuse.