The world consisting entirely of sky - is it possible? This is a setting for sci-fi novel The Integral Trees, written by Larry Niven in 1981. The concept is well worked out and is quite viable. There are calculational mistakes in it and some of them could kill the plot, or radically change it, but the model is real. This is how the Smoke Ring looks like from the far space:

Image: manoli_martin Neutron star Voy is in the center, gas giant Gold is vaguely seen in the Smoke Ring in the bottom right corner. Regretfully, author did not paint The Blue Ghost - radiation flows from Voy's magnetic poles but it does not influence the system - it is just beautiful. The main sun of the system is in upper left corner.

The Smoke Ring is really big. It is a central part of the Gas Torus circling an old neutron star Voy. The orbit of gas giant Gold is located just outside of Voy's Roche Limit which forces it to loose atmosphere and tears off parts of the planet. Being so close to the high gravity of the neutron star gases and minerals cannot escape to the space and lock the orbit - Gas Torus. The central part of the Gas Torus - the Smoke Ring, - has a breathable atmosphere, able to support life.

Image: Tom Calbfus - In the original novel the distance from the Voy to the inner edge of the Smoke Ring is 26 000 km what is clear miscalculation. In this case, to get 2 hours orbital period the mass of Voy must be not 0,5 solar mass but 1/100000 which is unlikely for the neutron star. But if the distance is 260 000 km then according the above formula we get orbital period about 53 minutes.

So the world of the Smoke Ring is endless sky where all life forms live in effective zero-g gravity except for edge cases.

Image taken from here but page's owner says he does not remember where it is from. Googling does not help.

Image: Michael Whelan. The water ponds in the Smoke Ring - free floating globes of the water

Tre travels in the Smoke Ring are dangerous. If you go wrong direction you can get out of the breathable zone and die, or fall to the Voy, or to The Gold. Another dangerous places - Lagrangian points of Gold where asteroids are. All Ring's dweller know well the old saying:

East takes you Out,

Out takes you West,

In takes you East,

Port and Starboard bring you back

Imagine yourself in the Smoke Ring with a jet pack or with a large fins so you can move in the air currents:

Image: ANDREW E. LOVE JR

An explanation of the saying given by Andrew E. Love Jr.:

If you apply a thrust eastward (in the direction of your orbit), you put yourself in a higher orbit (you move Out)

If you apply a thrust Westward (against the direction of your orbit), you put yourself in a lower orbit (you move In)

If you apply a thrust outward, you put yourself in a slower orbit, so you move West relative to everything else in your old, faster orbit

If you apply a thrust inward, you put yourself in a faster orbit and you move East relative to everything else in your old, slower orbit

If you thrust to the left or right, you move to an orbit that is at an angle to your original orbit, but which intersects your original orbit at two points, one of which is the point at which you applied the thrust - hence you come back to where to started after one orbit.

If you know well the rules and can survive in the Ring, but you are bored with zero-g, you could dwell on integral trees - giant floating plants named so because they are looking like the sign of integral.

Image: ANDREW E. LOVE JR

The gradient of Voy's gravity is so great that the opposite ends of the tree feel different tidal accelerations. Anything attached to the upper end of the tree is moving too fast for its orbit and thus feels an acceleration outward. Meanwhile, anything attached to the lower end is moving too slowly for its orbit and is accelerated inward towards Voy. The middle of the tree remains in free fall (otherwise the whole tree would accelerate into Voy or out of the Ring) - it's in the right orbit after all. Another way to think about it is that the whole tree is being swung around Voy, which should result in a centrifugal force outward on any object on the tree, but the gravitational force of Voy cancels out the centrifugal force exactly at the center of the tree, too much on the inner tuft and not enough at the outer tuft.

In the novel trees are up to 100 km long and have on the end gravity 1/5 g. Unfortunately here is authors's miscalculation, probably the same as above. Formulae give 33 g on the ends. It could be easily corrected - just to make tree shorter, but it kills the long and dangerous adventures of the humans along the tree. Nevertheless, if the trees are 100 meters long it's OK.

Image: Image taken from here but page's owner says he does not remember where it is from. Googling does not help.

Anyway, the novel (in fact it is trilogy, but I've read only first part) is highly recommended.

In the last decade more than 1000 exoplanets were opened even while we have not seen not a one directly. Who knows what strange structure, maybe even able to support life could exist in the Universe.

Sources:

[1] Larry Niven The Integral Trees

[2] The Universe of Larry Niven

[3] http://go2starss.narod.ru/sem/S014_buassard.html (in Russian)