I think by now it's pretty well established that, in a sandbox-style campaign, referees need to be prepared for players wandering off to do something or go somewhere you hadn't expected. Judicious use of random tables, swiping ideas from pre-made modules, and good old fashioned quick thinking all help in this regard, as does jotting down germs of ideas to which you can turn for inspiration all help in this regard. I've used all of these techniques in my Dwimmermount campaign and there are many others too, depending on how much preparation the referee is prepared to put into his campaign. (I veer toward a very low-prep style, so nearly everything my players do unexpectedly is met with an extemporaneous response rather than something I'd thought deeply about beforehand, though there are exceptions)
A question I don't often see discussed, though, is how to deal with players who show complete disinterest in what you've placed before them. Even diligent, well-prepared sandbox referees (i.e. not me) have limits to how many lairs, encounters, clues, rumors, treasure maps, and hooks they can place before the players. After a certain point, a referee is being reasonable to expect that at least one of the things he's created will generate some interest in his players and thus provide a segue to adventure.
I suppose I've been lucky in that I've never encountered such intransigence from my players, but I have observed it in action several times. In most cases, the players are not so much disinterested in the obvious options placed before them but rather unhappy that the options placed before them all seem to take them to the same place. In my experience, players dig in their heels when it looks like the all their choices are false ones intended to lead them back toward something the referee really wants them to do see or do. I recall one memorable failed campaign where the characters became so unhappy with an NPC whose answers were so clearly designed to get them to take up a course of action they didn't like that they trapped him, along with many other innocent bystanders, in an inn and burned the place down. So great was the players' unhappiness that even the player of the paladin looked the other way while his comrades committed mass murder.
In the Dwimmermount campaign, there was only one thing I planned extensively beforehand and that was the mystery behind the cult of Turms Termax. In planning the game, I'd hit upon an idea I really like and thought would make a great MacGuffin, something that would encourage the players, through their characters, to delve more deeply into both the dungeon and the world of which it's a part. To my pleasure, it's largely worked and, while I continue to add and subtract elements from my original idea in response to events in our sessions, the core idea has remained the same.
Now, if the players had not responded as I'd hoped they might, what would I have done? I can't say for sure, because, as I've said, I've never experienced a case where the players wholly rejected what I set before them. I'd like to think, though, that I'd either have reworked my idea so that it'd have become more attractive to the players (this is a practice I've used before) or that, if they really demonstrated an utter disregard for the mystery of Turms Termax, I'd have dropped it and found something else to engage their interest.
The willingness to drop elements from a campaign (or at least diminish their importance) is, I think, an important trait in running a successful old school sandbox campaign. No matter how good I think my ideas are, it's ultimately the opinions of my players that matter most. If they're not interested, there's little to be gained -- and much to be lost -- by forcing something on them. I try to remember that ideas are cheap, but player interest is often priceless. For some, it can be a hard lesson to learn, but, once understood, it more than repays the time and effort spent acquiring it.