The Long Sheet by William Sansom. I read it in the anthology The Weird by Ann and Jeff VanderMeer. This anthology was published in 2011, but the story was written in 1941 so you could certainly have read it in the 1970s.
The story starts:
Have you ever wrung dry a wet cloth? Wrung it bone white dry – with only the grip of your fingers and the muscles of your arms? If you have done this, you will understand better the situation of the captives at Device Z when the warders set them the task of the long sheet.
You will remember how, having stretched the cloth between your hands, you begin by twisting one end – holding the other firm so that the water is corkscrewed from its hiding place. At first the water spurts out easily. But later you will find yourself screwing with both hands in different directions, whitening your knuckles, straining every fibre of your diaphragm – and all to extract the smallest drop of moisture! The muscle of your arm swells like an egg – yet the wet drop remains a pinhead! As you work the cloth will gradually change from a grey colour to the whiteness of dried bone. Yet even then the cloth will be wet! Still you will knot your muscles; still you will wrench away at the furtive damp. Then – at last! – you will believe the cloth to be dry…but in the next second the tip of a finger will quiver tragically as it touches some cold, hidden veil of damp clinging deep down in the interlaced threads.
Such, then, was the task of the captives.
The container the men are is described as:
They were placed in a long steel box of a room with no windows and no doors. The room was some six feet wide and six feet high; but it ran one hundred feet in length. It resembled thus a rectangular tunnel with no entrance and no exit.
It is, as you say, a very odd story. The point appears to be made in the final paragraphs when a group of the prisoners have finally managed to wring their cloth dry:
Gradually these people achieved their end. In spite of the steam, in spite of the saturated birds, in spite of the waterous contagion seeping through from the room of the defeated, in spite of the long hours and the heat and the squared horizon of rusting steel – their spirit prevailed and they achieved the purity they sought. One day, seven years later, the wet grey sheet dawned a bright white – dry as desert ivory, dry as marble dust.
They called up through the skylight to the warders. The grave faces appeared. Coldly the warders regarded the white sheet. There were nods of approbation.
‘Freedom?’ said the captives.
The guards brought out their great hoses and doused the white sheet sodden grey with a huge pressure of water.
‘You already have it,’ they answered. ‘Freedom lies in an attitude of the spirit. There is no other freedom.’ And the skylights silently closed.