MDBG's definition of 癌 says:
cancer / carcinoma / also pr. [yan2]
MoE put their main pronunciation of 癌 as:
yán
Which might make it look like a TW thing but 兩岸's entry just reads:
ái
When and/or where is 癌 pronounced yán?
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Never heard of it. – fefe May 23 '18 at 5:34
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Some HK tv program say yan. – Jacob May 23 '18 at 6:26
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Not used today because it sounds the same as 炎(inflammation) – Jason Swift May 23 '18 at 6:35
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Taiwan people prounce it that way, and in China mandarin context it's always ái. – user19549 May 24 '18 at 5:28
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It reads yán in older generation in my hometown when I was young, but totally changed to ái currently. – 賈可 Jacky May 25 '18 at 2:35
From 神農氏
中國傳統醫學對癌症的描述. 癌，系由古代巖、岩、嵒等字轉化而來。因癌瘤之形如岩石，累累堅硬，高突不平，故取其音義而名。
In Chinese traditional medicine, cancer is described as like rock (岩), so it is pronounced as [yan2].
From Wiktionary,
In Mandarin, this character used to be pronounced identically as 岩 (yán). Its pronunciation was changed to ái in December 1962 to avoid the homophony between 癌 (“cancer”) and 炎 (yán, “inflammation”) (compare 肺炎 (fèiyán, “pneumonia”) and 肺癌 (fèi'ái, “lung cancer”)). The new pronunciation ái stems from dialectal pronunciations of 岩 (“rock; cliff”) /ŋai/, influenced by 崖 (yá, yái, “cliff”).
More info in Traditional Chinese
癌，在不同的地方有不同的讀音。在廣州話地區，它的粵音讀如“岩”，取“喦”之讀音；在內地，它的普通話讀如“皚”(ai)，即“埃”的第二聲；在台灣，它的國語讀音即讀如“岩”(yán)。
為甚麼“癌”字的讀音會有這些差異呢? “癌”字的最早注音，見於《中華大字典》：“癌讀若嵒。”一九一五年版的《辭源》，也注為“讀如喦”。喦，即岩的異體字。粵音據此一直至今都讀如“岩”。國語也曾一度據此讀如“岩”音。一九二一年，由民國政府的“國語統一籌備會”(魯迅也是該會會員)所訂正的《校改國音字典》，依然將“癌”的國音訂為“碞”。“碞”也是“岩”的異體字。直至今日，台灣也是按照這種讀音，沒有改變。
那麼，內地的普通話為甚麼又要把“癌”字改讀為“皚”音呢? 它又是甚麼時候改讀此音的呢? 原來，內地一直到一九六一年，都是把“癌”讀如“岩”的。當年, 新華字典大修，編者考慮到普通話中的“癌症”和“炎症”讀音完全一樣，容易造成混淆，故參考某些方言的“岩”字讀如“崖”音，於是便推薦“癌”讀“皚”音。一九六二年修訂的直排本《新華字典》，便將“癌”的國音注為ái，並用括號說明“舊讀yán”。一九六五年和一九七三年兩次印行的《現代漢語詞典》試用本，也都把“癌”字的注音改成“ái，(舊讀yán)”。
當時採用的這種注音方式，有兩個用意：一是表示ái，這個音不是印錯了，而是有意推荐的跟舊讀不同的音；二是表明，如果你不贊同ái的音，也可以讀舊音yán(岩)。
林語堂主編的台灣一九七二年版《當代漢英詞典》，一方面堅持“癌”的舊讀yán，另一方面則注明有人主張讀ái，用來跟“炎症”的“炎”區別。態度十分客觀。
到了一九八五年十二月，國家語言文字工作委員會、國家教育委員會、廣播電視部聯合頒佈了《普通話異讀詞審音表》，進一步取消了“癌”字的舊讀yán，統讀為ái。
至於粵音，由於“癌”與“炎”的讀音不同，不會混淆，所以毋需改讀，仍照舊讀如“岩”。
My dictionary (《现代汉语词典》) says:
旧读yan2
Which means it used to be read as yan2 in the past.
I don't know how long ago when the "yan2" reading disappeared, but currently the pronunciation is not used.
I personally never heard of the reading of "yan2" in my entire life. Only found it when I checked the dictionary.
