"The man sleeps."
Translation:남자가 잠을 잡니다.
No; at least in the formality level of speech that ends verbs with -ㅂ니다 (called hasipsio-che, 하십시오체), particles are never optional. However, at least in modern 한국어, it seems that 잠을 can be omitted. You can just say 남자가 잡니다. Just like how an English sentence doesn't mean the same thing if the words are in the wrong order, Korean grammar requires the use of particles in most cases.