The "can't melt down" property is usually referred to as "passive safety": https://en.wikipedia.org/wiki/Passive_nuclear_safety . These tend to have components that cause all of the nuclear fuel to passively flow out of the reactor and into a cooling chamber in the event of coolant failure. In liquid-fueled designs, this is accomplished via a "freeze plug," essentially a cork made of a low-melting-point material at the bottom of the reaction chamber that's kept solid by active cooling and rapidly melts in the event of a power failure such that the reaction chamber drains. Equivalent mechanisms exist for pebble bed reactors, though, where all the pebbles fall into a cooling chamber. In either case, production reactors have been build that include these features and the physics are very well understood.

Proliferation resistance is trickier, and not all gen IV designs focus here. There are a couple of areas of attention here. The first, and probably more mature development-wise, are alternative fuel cycles like the Thorium fuel cycle that don't produce easily usable fissile material out the other end (and do produce a bunch of U232, which in addition to being non-fissile is also difficult to steal because it's super-dangerous to handle). Secondly, there are designs that breed and then immediately burn fuel in situ without reprocessing, such that there's no point during which the fissile material exists outside the reactor to be stolen. I don't think any of this class have actually been built yet, but the Traveling Wave design is probably furthest along, and TerraPower is building one of those in China with a target completion date of ~2025.

Two important caveats though: these are "proilferation-resistant" in the sense that fuel would be hard for non-state actors to steal; state actors are another concern as that article points out, but they also don't really need to breed fuel, and can just enrich uranium directly without that much difficulty, as Iran and North Korea have both demonstrated, if they're willing to pay for it. At this point the physics are very well-understood, so this is a problem in need of diplomatic solutions more than technological ones. And second, the focus here is on material for fission weapons. I don't think any nuclear technology has good defenses against using material for dirty bombs.

All of that said, I'd still stand by my original point that newer designs are well-understood and dramatically better in these respects than most currently operating plants, and are only not being built (at least in the US and Europe) for political reasons.