I heard something different from what /u/Peachadee answered. I heard that cockroaches, like many insects, move their legs through hydraulic (pressure-driven) action. By default, their legs are fully contracted and curled up under them, and they have to intentionally relax them to move around. When they die, their legs contract, which often flips them over onto their back.
Someone asked this not so long ago. The top comment said something along the lines of that it’s not that hey die belly up. It’s that just when they are belly up they are very likely to die of starvation.
They walk on their legs, and there is plenty of space under eat them, so their centre of weight is quite high. If they flop on their back while in the grass or a carper or whatever, they can use their legs to grab something around them and position themselves correctly. But if they die on a flat surface, like an asphalt road, there is nothing they can grab, and so they die.
Edit: found the post/comment I mentioned
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byu/Champion282 from discussion
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