There's no real way to make chutes safe that I know of. Safety CAN be dramatically improved by using flowing water to shunt items from the drop zone over one tile, and most the time the dwarves wont be quick enough to grab an item before the water conveyor-belt moves it (and you can completely stop them trying with burrows). A water shunter requires a pump, and a power source (but it can power itself). It can recycle the water. But it has one significant limitation - it can't move heavy objects very well. Anything of weight 100 or higher, which includes stones and many corpses, wont be quickly moved by water, if they're heavy enough they might take like a season to be finally moved. That aside, it works great for anything lighter than 100 (for reference, a very heavy dwarf, can weigh over 100), and in some cases, even half a season's delay may not actually matter, like with mass ore dumping.
Here's the required layout.
o%%+GD+
inlet->pumpPump->Floor->Grate->Downstairs->Floor
Grate is drop-zone. Downstairs and floor on right is stockpile. The pump impassable tile, floor, grate and downstairs should all have walls along the side.
The level below the pump input and below the grate/downstairs should be linked to allow water return. A straight route may not be best, you should probably loop it around to allow build a waterwheel on it, and you want it deep enough so the water under the grate/downstairs is 7/7 (if it's less, it'll leak some water, but will also double as a mist generator)
Now note that this uses bizzaro-physics to work. The drop-zone is the grate, that's where items land. The pump causes water to flow across the floor and it falls down the grate. Here's where the bizzaro-physics comes in. Even though the water *disappears* on the grate tile, the game KNOWS that water is flowing from left to right (in this case) over that tile, so any items on the tile get moved to the right by the flowing water, even though the water isn't actually flowing to where the items end up. Items are actually pushed onto dry tiles.
Now I personally wouldn't bother building one of these things, but if you do want to shunt things which aren't stones as a part of a fully automated "supply chain" type thing, and don't want your dorfs getting clobbered to death by falling pieces of cloth... then it will work. Fantastically. And it's actually not difficult to build. One pump, one water wheel - and it's self-powering and doubles as a perpetual motion machine. There's also no reason in principle why it couldn't use magma, because the items get shunted onto a dry tile, so it could also sort goblinite for you.