>>401
In the example of 「彼は死んでいました」, there is a large difference between how some actions or states are viewed in Japanese. Take for example 「結婚する」.
To say "I am married", the present progressive is used: 「私は結婚しています」. It would obviously be incorrect to translate this in a direct way as "I am marrying". Likewise, the sentence: 「隣人の犬は死んでいる。」 does not say "My neighbor's dog is dying" but rather "...is dead". In the past progressive 死んでいた is translated as "...was dead".
I can't speak for the exact reasons but, in a way, the present or past progressive form sometimes describes actions or states which aren't thought to be properly "completed" in a certain understanding. I would focus less on trying to make a verbatim translation from Japanese to English by tacking "ing" onto any te-iru constructions you see and instead refocus on how to get a general estimation.
I've personally seen the Japanese past progressive of some verbs translated in the English perfect verb tense (a decision with which I usually agree). Your sentence would then become "I had completely forgotten that my friend was coming today". Though in English "had forgotten" is seen as perfect, not continuous, you can hopefully begin to tell how it might work as a past progressive action in the same sense as marriage and death. If not, take it with a grain of salt.