Two pieces, and the second one is the whole picture: off plus line. Think of a line running out of something and joining it to everything else — a cable out of a printer, a phone reaching the network, a conversation everyone in the room is plugged into. Being offline is down off that line. What changes across the senses is only which line is meant. Take away the internet and you get the everyday meaning. Take away the cable and you get the printer that will not print. Take away the shared conversation and you get the meeting-room slang. In every case, the thing is still there; it is just no longer joined.
From the word’s history
Wiktionary gives the formation directly: off- + line. The word is built, not borrowed, and the two pieces still carry their ordinary meanings, which is why the picture above works for every sense.
來源字典直接寫明構成方式：off- 加上 line。這個字是組出來的，不是借來的。兩個零件到今天都還保有原本的意思，所以上面那張圖對每一個用法都成立。
Wiktionary (kaikki extract), entry 'offline', etymology_text: From off- + line.
登入就可以看每一支怎麼連回核心畫面。