Not fasting without a valid excuse is a major sin. What this person must do is fast with the people of his city, even if he conceals the fact that he is fasting or spends most of the day outside the house, so that none of his family will notice that he is fasting. If he was afraid of being found out and he cannot find any option except not fasting, then there is no sin on him, and he only has to make up that fast.
Al-Hafiz ibn Rajab al-Hanbali said: Moreover, there is a difference between one who does not pray and fast at all and one who starts to do them then renders them invalid.
The latter has to make up the invalidated act of worship, like the one who renders his Hajj invalid. The former is like one who is obliged to do Hajj and did not do Hajj; rather he should do Hajj after that, because Hajj is a once-in-a-lifetime obligation.
The view of the Zahiris (literalists) – or most of them – is that the one who did that deliberately is not required to make it up. That was narrated from [Abu] `Abd ar-Rahman, the companion of ash-Shafa’i in Iraq, and from the grandson of ash-Shafa’i [his daughter’s son]. It is also the view of Abu Bakr al-Humaydi regarding fasting and prayer, if a person deliberately did not do them, that it is not valid for him to make them up. Something similar was said by a number of our earlier companions, including al-Jawzjani, Abu Muhammad al-Barbahari and Ibn Battah.
End quote from Fat-h al-Bari, 3/355.
What appears to be the case is that the person asked about comes under the ruling of one who has a legitimate excuse, not one who does that deliberately, and we hope that there is no sin on him. He must make up the fast, but he does not have to offer any expiation.
See also the answers to questions no. 234125 and 106476.
And Allah knows best.
