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If there is a hold timing violation, the FF can't capture the input data right, the same as setup requirement. So, setup/hold check will mae sure that FF capture the input data right.
The hold time for a sequential cell is the minimum length of time the data-input signal must remain stable after the active edge of the clock (or other specified signal) to ensure correct functioning of the cell. The cell is considered functional as long as the delay for the output reaching its expected value does not exceed the reference delay. So, if there is any hold violations, you will not get the proper functionalty. There will be certain functionality failure.
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