I would use the commas.
Eileen(,) whose dog is lost(,) is depressed.
Are the commas optional?
Thanks.
I would use the commas.
Otherewise it sounds like you have a bunch of women named Eileen and you're using "whose dog is lost" to identify which of them you mean.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
You could use dashes or parentheses, so no they are not mandatory. But some parenthetical isolation of the dependent clause is required. In fact the comma pair proposed are merely an adaptation of the most suitable punctuation for such cases, the parentheses. They are, in fact, called parenthetical commas. ;)
He's saying, simplifying a little, that I was wrong in saying that the commas are mandatory because you could write "Eileen (whose dog is lost) is depressed." or "Eileen - whose dog is lost - is depressed." instead.
By the same token, I guess, the commas are not mandatory because you could write, "Eileen is depressed because her dog is lost."
However, it remains that if the two choices are i) that sentence with commas, and ii) that sentence with the commas removed and nothing added, the only correct choice is i) - which is what I meant by calling the commas mandatory.
Thanks, Raymott, for the detailed explanation.