jsiehler, excellent answer and well worth a lingot so I'm giving one. I had exactly the same notion but he/she beat me to it. mögüle = from behind so belőle = from within just as előle = from in front. It's just that translating literally "from within" doesn't always work very well. It's the thought process to begin with and then it's a matter of looking for a phrase which means much the same but sounds reasonable in English.
belőle = "from within it", either physically (from within an enclosed space) or metaphorically (like strength that comes "from inside you")
tőle = "from it" more generally. In a location sense, it means "from its general area." It can also mean "from" as in receiving a gift or a letter from someone.
Yes, there are actually a lot of little irregularities in how the personal forms of these endings are constructed. Among other things, it seems nearly random whether the front-vowel or back-vowel version of the ending gets used to construct the personal forms. Tőlem but nálam and hozzám; belőlem and belém and bennem but rólam, rám and rajtam; and so on.
That's just how they are.
Why do you need to? Why not just say ‘something comes from him’? Or why not add ‘ki’ just to help people learning Hungarian. After all, I’ve heard all sorts of mangled English sentences deemed as correct just because they’re exact translations of the Hungarian sentence. In stead of being petty, why not help the learner
The sentences in this section are weird anyway. :´)
Okay, so "Something comes from him" is a more ambiguous sentence, it could mean either belőle or tőle, maybe even felőle. "Out of him" can only be the former. Jsiehler above also mentions "from within", which should be appropriate here, too.
The Hungarian sentence could use the ki- prefix, but in this case it might be better without. With "valami jön ki" it sounds like you approximately know what it is, you're able to determine its size/amount, so you know when it "stops coming out". If you're using a verbal prefix, the action has to have an end point.
For instance, I would use "Valami jön belőle" if you're talking about a liquid (in the process of) leaving a body, and "Valami jön ki belőle" if it's an animal leaving a cave.