[elhigh]

The speed does double. One wheel fixed and one wheel free, the free wheel will turn at double the differential's speed.

The ring gear is attached to the spider carrier. Normally, with both wheels on the ground, everything turns at the same rate: the ring gear/carrier, and the axle gears are all moving along. In a turn your speed doesn't change because, as one wheel must necessarily slow down on the inner, smaller circumference of the turn, the outer wheel must speed up for the outer, longer circumference. The increased torque on the inner wheel gets multiplied into greater speed on the outer wheel. Net torque applied to the drive wheels remains the same (minus the gearing losses) and your speed through the turn doesn't change.

With one wheel in the air, that wheel turns at double speed, so if you rev the engine and see it indicating 30mph according to the speedo, the wheel is turning at 60mph worth of revs. As the spider gears are attempting to push the fixed axle - and failing - those gears are also turning. So in addition to the revs applied to the ring gear turning the free axle, the spider gears rotating against the fixed axle are also pushing the free axle even further. Double speed.

Very simple demonstration:

Drop a rolling pin on the floor.
Drop a 6' long board on the rolling pin. One end right there on the pin. Mark the spot on the floor where the handle of the pin is, call that 0 feet. So the end of the board and the pin are both at 0 feet.
Push the board forward, rolling on the pin, until its other end drops off the board.
Where is the pin? Six feet from where it started.
Where is the far end of the board? TWELVE feet from where it started.
2:1 ratio. The board is one axle gear, the floor is the other, and the rolling pin is the spiders. Now wrap it all up into a circle and the floor is your fixed axle and the board is the free axle, and instead of pushing the board you push the pin. As it goes around, it moves the board forward at twice the pace.

In order to see something besides 2:1, the axle gears would have to have different tooth counts. You will never ever ever see that. For one thing it would make the spider gears VERY unhappy, and for another it would make the car behave differently turning one way vs. the other way, which would make YOU very unhappy.

Hmm. There is a way to see a different ratio. If the car is running a "spool," which is to say the axles are fixed directly to the ring gear and cannot rotate at different speeds relative to each other. You won't see that outside drag racing. If one wheel is turning and the other not in a situation like that however, that means an axle has snapped and you will hear lots of bad language.

NOW, regarding your original question: that will destroy a differential in fairly short order.

Those spider gears aren't really intended to work that hard for that long. You spend the vast majority of your time driving in a more or less straight line. The spider gears absorb little corrections as you're keeping it between the lines, probably not making a hundred full turns in total over a mile of typical interstate. And the net load on them is distributed evenly, you go to work and go home, making the same turns but in the opposite direction.

If you weld one output in place so the spiders are continually walking around it, overdriving the other output at a 2:1 ratio, then they will be put into a duty paradigm never imagined by the original engineers, and it will all be on one side. It'll get pretty darned hot inside that diff.

I have seen diffs fixed to act as spools, both as cheapo spools for drag racers on a budget, and in the bizarre-yet-awesome Amazonas motorcycle that used a complete (!?) VW Beetle drivetrain. The spiders were welded directly to the axle gear on one side, and a chain sprocket attached to the axle stub. Funky but functional. Funnier yet, that left reverse gear available and on a bike like the Amazonas, that could be pretty useful.