Daniel, mi compatriota, Dejar de meaning stop from doing something refers to the subject of the sentence. Dejé de fumar. To stop someone else from doing something, you could use impedir, evitar, prevenir, prohibir, depending on the context. Prohibo al perro que coma. Oh, that sounds weird.
Where I live we say we are leaving someone or something to do something in the sense of allowing them to. So if I say 'I'll leave you to it' I don't necessarily mean I'm physically leaving but that I'm letting you get on with it/not impeding or disrupting you. So that caught me out.
Reply this questions: ¿Quién va a dejar comer? ¿A quién va a dejar comer? You can see in spanish "a" points to the object. Then the answers are: "yo voy a dejarlo comer" and "a el perro". "A el" contracts to "Al". That is the reason. There are just a few contractions in Spanish, the other one I can remember now is "de el" to "del"
Note for people who know subjunctive or like to skip ahead. I just heard from one native spanish speaker (definitely not representative of all speakers, contexts, or regions, but better than nothing) that a more natural spanish version would be "Voy a dejar que el perro coma" though both are correct.