Looking for anthology story 30+ years old. A new man lands/appears outside castle/home of leader? and finds that the fabric of the old universe which is just ending crumbles when he touches it.
"Visiting Amoeba", a novelette by Brian W. Aldiss. Originally published (as "What Triumphs?") in Authentic Science Fiction #82, July 1957, available at the Internet Archive. Reprinted in various Aldiss collections; any of these covers look familiar?
"Listen to me!" you interrupted. "Those things belonged to a different principle. Watch this!"
You walked over to a wall. It was built of solid blocks of marble, polished and selected for their delicate patterning. You placed one hand with extended fingers upon it and pushed; when you withdrew your hand, five short tunnels had been pierced in the marble.
It was a simple demonstration. They were greatly impressed.
You wiped your hand and returned to them, but they shuffled away from you, their lips pale.
"Yet I am no stronger than you," you told them. "The difference is only this: that I come from a freshly created world, new minted by the inexorable processes of continuous creation. And you—you come from an old world. Think of your Galaxy. How old is it? You do not know exactly, but you know it is incredibly old. the truth is, it is wearing out, as everything wears out in time. Nothing is meant to last. Ask yourself what everything is made of. A tissue of energies which outcrops and becomes matter. That tissue of energy, since the beginning of time, has been running down, wearing thin. All matter, which is composed of it, has worn thin with it. The great magical batteries of your Galaxy are slowing, so all protons and neutrons lose their polarity. Their charges run low, they cannot combine as they once used to. Steel has not the strength that paper once possessed, wood is water."