From a conceptual point of view asserting both zx
and nx
is a bug in the microcode or control logic1.
What exactly happens is strongly micro-architecture specific.
We can however hypothesize a very simple machine, where
zx
enable the clear signal of the destination register.
nx
enable the data-path from the adder2 into the destination register.
At the next clock a register will be concurrently feed with input and asked to clear it self.
What it will actually do depends on the manufacturer, taking the first Google result for PIPO register datasheet3 we can see this table

When #CLEAR is active (it is active low), no matter the mode or input, the register is zeroed.
1 Unless zx
and nx
have a meaning together of course. For example selecting one out of four operations.
2 Assuming -A is computed as A̅ + 1.
3 It founds a 4-bit PIPO register datasheet.