I've been doing some thinking about how you might run an investigative game - Call of Cthulu being the paradigm example - in a sandbox style. The problem with that sort of game is that it is heavily reliant on the players responding to events rather than guiding them by themselves. Something, or somethings, have to happen for them to investigate, and by definition that means that the GM has to spend a lot of setting up quasi-railroads for them to follow.
I say "quasi-railroads" because providing players with something to do ("A young woman mysteriously disappeared last night and her mother asks you to investigate!") is not a railroad per se, but leads down a certain path which has only two outcomes - success or failure in finding out what happened. How you get from A to Z is not set, but you'll probably end up getting there in the end. And by the same token, you can create a huge rumour table all you like - a d100 list of strange occurrences for the PCs to delve into - but at the end of the day, as GM, you have to know where those strange occurrences lead: all you've done is create a list of 100 quasi-railroads, ultimately.
I don't think there is a way around the investigative/quasi-railroad problem - it is probably at its most pernicious if you want to run a police procedural, but it still means that any Call of Cthulu campaign is likewise going to be heavily GM-led, simply by dint of its nature.
One possible way to make a Call of Cthulu game more of a sandbox would be to subtly shift the starting assumption and make sure that the players begin with an understanding that their characters are deliberate seekers of dark powers and magicks who already have some idea that there is a wealth of forbidden knowledge out there - if they could only get their hands on it. Their investigations, in other words, would not be into mysterious events that the GM tosses their way, but an exercise in finding where all of this knowledge lies. They might start off in Providence, Rhode Island in 1922 with a web of contacts, and locations, which they can tap as resources in conducting their own self-centered investigations - my character has heard that it is possible to live forever, and now I'm going to find out how - and this would allow them to drive things along more autonomously.
This would require extensive preparation on the part of the GM pre-campaign - akin to the way I set up urban sandbox games in general (see entries passim here and here), only more so - and also a good, skilled GM who is able to think things up on the fly. As such it may be more trouble than it is worth, though I think it's something I could happily give a try to see what happens.