masonrypaversstone
I've got a limestone patio. The builder apparently didn't support one corner very well and somebody stepped hard on it and a triangle about 1/2 square foot in size broke off. I imagine putting some sort of concrete underneath it but I'm not sure what product to use, or even if this is a good idea or if there's other things I should worry about.
EDIT: Here's a photo: 
You may have to dig deeper depending on where you want the pavers to sit (at ground level, slightly above ground level), and how thick the pavers are. You'll want 5-6" of the base material, plus 1" of sand, plus the paver thickness (keep in mind the 1" of sand may compact a bit when you set the pavers, and after the final tamp).
To make the job easier, you might want to rent a Plate Compactor this will make tamping the base material easier and help lock in the pavers after you sweep the sand in the joints.
Typically when you build this type of "patio" you'll have to worry about drainage, so you'll want to slope the whole thing enough to allow the water to run to a safe location. In this case you probably won't have to worry so much, unless the patio is right up against the house.
There are epoxy products that can be used to repair stone, such as this one
This will work to glue the seams of the big chunks back in place. While it could be used to fill other breaks or gaps, it probably will not look very attractive.
Also, as DA01 says in his comment, the overhang makes this a very vulnerable area. Usually stones which overhang have a thicker dimension.
There is not too much you can do unless you want to put a facing under the overhang to help support it, a fairly big job involving cutting strips of matching stone. You could watch for the beginnings of cracks near the edges and fill them with an outdoor epoxy based material. This will reduce the chance that water gets in them and freezes, which leads to major cracking.
You could also tread lightly on the edges.
Best Answer
I am really not sure what your patio looks like. I am going to assume it sits on the ground.
It would be normal for a lot of the erosion of the patio to happen on the corners. You have basically two options...
Compress ground. You need to wet the ground around the area to make sure there are no gaps with weight. The pavers shouldn't be hanging above ground at all. If this is the case then you will have more that breaks. An easy fix would be to get some fast setting quickcrete... Build yourself a box to meet your needs - you will probably need 2 pieces of 2x6. Fill box with the quickcrete and try to push the quickcrete under the adjacent paver piece if there is a gap. Just level it out to fit your needs. Pour slowly so you don't have to cup any out.
Remove the current piece. Keep removing pieces until entire paver lays very flat on the ground with absolutely no gapping. Add more dirt/rock and then compress and reinstall pavers.
Based on picture I would carefully knock off as much of the cement as possible inside the boxed corner - if that makes sense. Really I don't understand the lip. Maybe it looks good but will increase chance of stone cracking. I would then refill with a quick set concrete. It needs to be filled right. You see yours is uneven probably helping the break. I would then put that corner back on... I know you will have a little crack showing but taking a sheet out will be a pain. I would then fill the crack with a knife grade epoxy - should be fine with limestone. Since your color is lighter and very neutral I would not color the epoxy or it might stand out more.