What words exist that come from deconstructed characters?
look for "拆字" (roughly destruct character), particularly fortune telling story.

水巷 --> 港

卯金刀 --> 劉

several verses from a famous oracle poem in hong kong, 1933:

"人我太陽爭北土"

人我　--> 俄羅斯 (russia)

"十四一心人發奮．水去西方啟戰爭"

十四一心人 --> 德國 (third reich, at that era)

水去

"晉有出頭寧坐視．中央生草不堪耘"

晉有出頭

中央生草

guess these five characters?

edited.

another word to look for is "離合", there're many examples in literary of yore. e.g. the wiki had 古今譚槩, in volume 29, "談資部":


  「取上一字，下拆兩字，字義相協。」倡云：「山上有明光，不知是日光、月光。」文云：「堂上掛珠簾，不知是王家的、朱家的。」陳云：「有客到舘驛，不知是舍人、官人。」王云：「半夜生孩兒，不知是子時、亥時。」各賞大觥。


in which the condition is choose one character (取上一字), break it into two (下拆兩字), and then the character, its meaning is in accord (字義相協).

four persons done it :)

山上有明光，不知是日光、月光 (明 --> 日, 月)

堂上掛珠簾，不知是王家的、朱家的 (珠 --> 王, 朱)

有客到舘驛，不知是舍人、官人 (舘 --> 舍, 官)

半夜生孩兒，不知是子時、亥時 (孩 --> 子, 亥)

it might be too difficult for elementary learners, or simplified chinese users. but, it's the funny, witty aspect of the traditional culture.