Suffosion is the mechanical relocation of fine particles by pore water. Fine grains are transported underground through the existing pore area, while the matrix of the bigger particles remains untouched. This kind of processes happen in karst but is not restricted to soluble rocks. It is also common in soils and soft sandstones. In this case it is called suffosional pseudokarst, as it is the development of caves and dolines as a purely mechanical process. Pseudokarst features have the appearance of karst landforms but are formed by processes other than bedrock dissolution. It is possible in all granular aquifers, in other terms in porous rocks where the groundwater flows slowly through the pores of the rock.
A Piping Cave is a cave which is formed in unconsolidated clastic sediment or unconsolidated rock.
The common english term for this type of cave is piping cave, but that term does not explain what it is. Any cave is a sort of pipe or passage. That's the reason why we find the name claystone cave easier to understand, because it actually contains the most important fact about this type of caves in the name. These are caves formed in claystone, in more or less unsolidified clay, soil, or loose sediments. These caves form in dirt, not in rock.
Piping caves are very rare, to make that clear right at the beginning. This is due to the fact that very exceptional conditions must come together, a sufficiently large amount of unconsolidated rock, a climate that is conducive to the formation, and finally an unconsolidated rock that has very specific properties, primarily stability. The vast majority of unconsolidated rocks are simply eroded by water, i.e. removed and transported to another location. The longest piping cave is currently B&B Caverns in New Mexico, U.S.A., which is 821 m long and 325 m deep . The vertical range is not bad, but the length is ridiculous. So there are cave systems with 500 km in length and this cave is 800 m long. But the reason why they were overlooked by speleological research for centuries that they are found mainly in arid areas and these have been studied more intensively only in recent decades.
Water and unconsolidated rocks normally gives mud, think of a muddy tidal wave rolling through a valley. Only if the unconsolidated rock has a gap through which water can penetrate and the water then provides this removal underground can a cave form. The geological process is erosion, so it is a form of erosional caves. Since this process is very fast in unconsolidated rocks, cave formation and destruction also happens very quickly. Such caves are generally young, and only in areas with arid or semi-arid climate one can hope to find such caves. Only there rainfalls are rather rare and the cave survives at least long enough to be safely explored.
Typically, they form along steep-walled valleys where water enters a fracture above and near a valley. The water first loosens the materials in the fracture, then washes it down and out of the base of the valley wall. Such caves usually have a substantial vertical section, in some circumstances they can be nearly horizontal.