I led with this phrase because it’s a little time bomb: what does “cheap” mean? —”inexpensive”? “penny-pinching”? “not willing to spend the money for quality”?
Those possibilities energize today’s Horror. Here’s the whole sentence:
“Parents often take children to fast-food restaurants out of convenience or because they are cheap, something rare in this economy.”
Well, when we tumble into the “something rare” modifying phrase, we might find some clarification. After all, if “they” is parents, meaning that parents are cheap, then the statement that cheap parents are rare in this economy is confusing. In this economy, I would think, cheap parents are increasingly common, not rare, except possibly among the One Percent.
That leaves us with what the student almost certainly meant: fast-food restaurants are cheap. And maybe all the definitions of “cheap” work for this one: inexpensive because penny-pinching and not willing to spend the money for quality ingredients or quality chefs or quality ovens or quality cookbooks.
Just the same, even after acknowledging that that’s what the student meant, I go back to the beginning, start reading again, and still find myself reading about cheap parents. I think the problem actually lies in the first adverb: “out of convenience.” That modifies the action, but clearly by providing a motivation for the subject, the parents, to take the action. Follow that phrase with an “or” and you set up the expectation of a parallel—and there it is, another adverb. Yes, this time it’s a clause and therefore not really grammatically parallel, but that doesn’t defeat the expectation of parallel intention, and so the adverb clause can be assumed (rightly) to be modifying the verb “take,” and (okay, wrongly) to be providing a motive for the subject to take the action. With these assumptions as the set-up, “they” has to refer to “parents,” and “cheap” has to modify them.
Besides, we’ve all had moments when we thought our parents were impossibly, embarrassingly, or infuriatingly cheap. That fact probably confirms the assumptions in the thought process I’ve just described.
My recommendation is to ignore the final phrase in the student’s sentence and enjoy the laughter explosion caused by the little “cheap” bomb.