I answered a question earlier today. It asked something like for an element $g$ of a free group, does there exist a finite-index subgroup of the free group such that g is a basis element of the subgroup. The author seems to have deleted the question. I can't seem to find it in my history (but I switch computers frequently and don't remember which one I was using).
Can a moderator locate the deleted question? One concern of mine is that it would have been a pretty good homework question for an course in geometric group theory. That's the only real reason I can imagine it being deleted (since it had multiple upvotes when I answered it).