"They sleep without him."
Translation:One śpią bez niego.
After a preposition, you must use niego (all third person pronouns have a variant starting with n- in all cases except for nominative, and that variant has to be used after prepositions).
You use jego at the beginning of a sentence, or when you want to contrast between jego and something else. You also use jego as a possesive, a preposition doesn't modify it then.
In almost all other situations you use go.
Another similar three-form example is niemu/jemu/mu, dative of on/ono.
Forma „-ń” to krótka forma poprzyimkowa – tylko rodzaju męskiego. Piszemy ją zawsze łącznie z przyimkiem, np. „doń”, „zeń”, „nań”.
So instead of "bez niego" you could theoretically write "bezeń", which would probably sound quite poetic. I actually had to check if this specific word is even correct. Such things are faaaaar from the scope of this course. Like, really advanced level of learning Polish as a foreign language.