Some depictions and descriptions of a Dyson sphere use an opening at the north and south pole to dissipate the heat generated by the star.  Another uses a single opening as a method of propulsion.  A third uses a handwavium device to control the star's energy output.

As far as it being used to contain a planet that's a bit extreme in my book?  Such a drastic method would suggest that the planet itself is somehow infectious or cause harm to the surrounding solar systems (Chernobyl example).  Containment of a race would be far easier by use of an orbital array of satellites (Deep Space 9 had an episode using this method).

Now what might work is the Hollow Earth scenario.

An alien race builds a near earth size Dyson Sphere ship as a way of escaping from their sun going supernova.  The ship is of the sublight variety and takes thousands of years to reach another solar system.  They have conquered everything necessary to make the inside of the ship a working biosphere.  Instead of a star, they use a series of lights mounted in the center that mimic the sun's ambient light source, which would solve the overheating problem.

During it travels through normal space, the outer surface collects dust, ice and organic material. At some point, the ship's asteroid and meteor defense systems begin to fail allowing more material to collect on the outer surface.  After  'X' number of thousands of years the ship is finally captured by a star.  It just so happens to settle an orbit within the star's habitable zone.  The exterior of the ship is now covered in a thick layer of material and an atmosphere begins to form. At this point, an asteroid penetrates the hull of this causing just enough damage to the interior hull and allow the interior biosphere a chance to escape and populate the surface.

The genetically alter plants from the interior which make it to the surface, now spread rapidly as they mutate under the radiation of the primitive atmosphere.  Over the next few thousand years, the planet develops a true earth like atmosphere primed for habitation.

Scenario include:

1.  The ship is believed to be a planetoid and it's only after a mining corporation starts sink a shaft do they realize there is a hull under the newly formed crust.

2.  The inhabitants have made their way to the surface and the culture is divided between those who live on the outside and the inside.

3.  Instead of few thousand years, 10's of thousand years have passed.  Those who moved to the outside of the ship have forgotten that they are living on the outside and have no idea of the culture inside.

4.  The ship is believed to be a planet ready for colonization until some part of the ship is discovered leading the team to investigate the planet further.

5.  The inhabitants of the ship have no idea they are inside an artificial world having survived some catastrophic event which made them forgot their true origins.

Further adventure are possible...

Since Malcedon brought up the subject of ringworlds, I would like to suggest the following four  types of ringworlds.

1.  Larry Niven's Classic ringworld.

2.  Smaller free standing Ringworld. From the game Halo, a smaller version.

3.  Planetary Ringworld.  A ringworld around a planet in place of a moon.

4.  Ferris wheel.  From the movie Elysium.

1 and 2 are ringworlds designed after one designed by Larry Niven describe in his book.  1 is quite large and circles a star, while 2 is placed around a star within habitable zone.  1 used panels to create night and day cycles, while 2 uses its axis relative to the star creates the night and day cycle.  1 requires an entire solar system of material while 2 may only need several planet's worth or an asteroid belt.

3.  Smaller than 1 and 2, the ringworld orbits a planet and act's like the planet's moon.

4.  Smaller still, the space station in Elysium appears to have the attributes of a ringworld.  Ships can enter the living area by going over a lip which holds in the atmosphere.   A central hub provides stability for the ring as well as a equipment, landing and storage area.  Night and day cycles are provided by the station traveling around the planet.

AS he stated in his post, these type of ringworlds would be above SF tech Level.  Usage in game would be minimal considering that any such adventure would have to be a full blow campaign because of their size alone.

Book recollection alert! There was a book I read a long time ago where humans had found a world which was very large but had less gravity than it should but still more than one G. After all was said and done, (and it's probably telling I have NO idea what went on in the actual story) the characters find out the REASON is the "planet" is actually a containment for a blackhole which is where the gravity comes from.

IIRC the blackhole was also remotely powering the rememnts of the super-civilization that built the planet but not at all sure since I can't recall details.

Comment on the dual-surface word: After thousands of years the penatration does not have to be an asteroid. By that time I would figure all if not most of the original "locks" for different purposes. (The inhabitants may have forgotten they live on a starship but the orginal builders would have had a LOT of reasons to install them in the first place)

The main impediment of having "civilizations" on either surface is going to be a serious lack of materials for those inside and shortages for those outside once they get going anywhere.

Lack of a magentic field is going to be an issue for those on the outer surface as is atmosphere leakage and breakdown. I'd see an upper limit of 'habatiablity' being less than a thousand years easy.

Randy

http://gizmodo.com/a-new-type-of-dyson-sphere-may-be-nearly-impossible-to-1694258669

Here is an article that just showed up on Yahoo about dyson spheres...