shadow registers are used when we need to modify the read only registers. they help the programmer to keep track of what is written to write only registers
see this Registers and Processor modes The Read-Modify-Write problem
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The shadow register term appears also in retention flops.
The retention flops are type of flops which can save their info when power is switched off. To do that they have some ballon register or "shadow" register which has a constant power, and in power down mode that register remembers the flop data.