[ggm]

Its called "soft touch" plastic. Have a google search. To me, its almost like a crossover between suede and velvet. Very odd feel. I have a book about the design of the apollo era moon suits which is coated in a version of this over kaptan: the book dust jacket is both indestructible, and feels very sexy-odd. I almost can't pick the book up!

Half the hand weights at my pilates gym are coated this way. Some people prefer them, feel more "grippy" but harder to clean afterward than the shiny ones.

the problem you identify is the behaviour of the "plasticiser", perhaps (I am a non chemist but as I understand it) a specific component of the plastics design process, which takes a long chain polymer and makes it flexible rather than rigid. Its a physical mixture as much as a stable reaction outcome: its reversible in temperature and UV exposure achievable in ordinary life. Rigid plastics (urea formaldehyde?) degrade to a powdery surface over rigid form and become brittle. Soft plastics degrade by re-liquifying. Some nylon-like fabrics (Tents, rucksack straps) turn to dust.

In some cases, this thing comes out of "solution" and you get a really repellent outcome: The feet of a 1980s era modem I had, were soft plastic pads glued onto a steel chassis and they re-liquified into a black tarry mess.

My son's baby shoes, the first pair, the ones we kept, in a box, high in the linen cupboard? heat degraded the plasticiser and the soles turned back into little balls of plastic in a goopy blue honey-sticky mess.