long version:

inside the transfer box there is a diff, but this diff is mounted sideways and the input goes in one way and the output's go the other ways

so for starters the output shaft length from the gearbox is longer than the 2wd version and the case is a different shape so you can't just swap out parts

so now the output from the gearbox goes into this diff, in the middle and, through the wonders of gearing, it turns the output shaft of the box in the same way that you would use one of your wheels to spin up your own rear diff

this, as you would expect, then turns the wheel on the other side of the car 180 degrees to the input AND turns the diff crown wheel

the difference in a sideways diff is that the crown wheel doesn't turn a pinion shaft at 90 degrees, but rather the crown wheel turns a chain which then offsets the output to further outside the gearbox (which is why it's got a hole about 14 inches further outside the gearbox to drive the front diff)

this then all sounds brilliant, but as soon as you remove the front prop, all the turning from your output shaft is now going in the direction of least resistance, exactly like an open diff if you were to remove one of the driveshafts

but you have a viscous coupling in your box, which limits the amount of slip, which is why you call them "limited slip differentials"

so essentially by removing the front prop, you are loading up the centre viscous to max to drive the rear prop and this will overheat it and burn it out in a matter of minutes

when the front prop is connected, all the wheels are spinning at the same speed and so there is no requirements to load up the viscous and so it doesn't wear out

phew

i could go into this deeper with diagrams and stuff but i'll only do that if you want it explained further