Thanks for bring the question up, orbiter...
Thanks for the quick response to the question, 김 감독님...
I do think that the explanation of Sean is very good to understand but (if Sean lets me) I'd like to add some of points.
1. The definition of 빌어먹다
Yes, it is a VERB meaning "to beg; as the result of begging, being able to eat"
2. The definition of 빌어먹을
Yes, this word came from 빌어먹다. However, 빌어먹을 is an ADVERB meaning "Gosh, Shit, Dame it"
3. The other usage of 빌어먹을 - as an ADJECTIVE
As Sean mentioned above, if it is used with nouns such as 놈, 녀석 (for examples, 빌어먹을 놈 or 빌어먹을 녀석), it is used as an adjective describing the following noun. When you say "빌어먹을 놈" or "빌어먹을 녀석", it indicates that you are extremely mad at the 놈 or 녀석.
4. The synonym of 빌어먹을 - 제기랄
Both words, 제기랄 and 빌어먹을, are slang terms so please be careful with those words when to use them.
5. Some example sentences of 빌어먹을
a. 나 돈을 잃어버렸어, 빌어먹을 (제기랄)... "I lost my wallet, shit..."
b. 길을 걷고 있는데 갑자기 누군가한테 맞았어, 빌어먹을(제기랄)... "I just got beaten by someone (without any reason) while walking along, dame it!"
c. 아, 빌어먹을!!! 누가 내 주스를 마신거야!? "Oh no, shit! who drank my juice!??"
Just keep in mind this please!
This 빌어먹을 (or 제기랄) is a slang term, it's okay to use it to yourself but never to others.
I hope my explanation helps you understand the word better,
cheers,
Tim
감독님, 정말 감사드려요~~^^