Pulped-natural processing begins by removing the coffee cherry's outer skin, then drying the coffee with some fruit material still attached. It is often associated with Brazil and offers a useful contrast with drying whole cherries or washing away the mucilage before drying.
The remaining layer makes drying conditions and handling important. Producers need an appropriate drying surface, regular movement and a workable weather window. The source describes patios and raised beds, with mechanical drying also possible. None of those choices alone proves that a lot will be sweeter or cleaner than another.
When buying, look for information about the actual producer and process rather than treating pulped natural as a quality grade. The category can suggest a combination of sweetness, texture and clarity, but roast and brewing will change the cup. A measured comparison with a washed or natural coffee from a similar context is a better way to discover your preferences than assuming the processing label settles them.
The conversation
A good question can make a better brew.