expression, godan verb (-ru)
lose one's appetite; eat less
Describes a decrease in appetite, often due to illness, aging, or worry. The subject is usually a person.
最近、父は食が細ってきた。
Recently, my father has been losing his appetite.
暑さで食が細る。
The heat makes me lose my appetite.
食欲がない simply states 'have no appetite', while 食が細る implies a gradual decline or a tendency to eat less.
Compound of 食 (しょく, 'eating') + が (subject marker) + 細る (ほそる, 'to become thin, decline'). The verb 細る here figuratively describes appetite becoming 'thin' or diminishing.