Is it really threshold voltage (MOS diode) or is it forward
voltage of an actual PN diode? There would be different
causes.
And of course every lateral diode has a (field or thin)
MOS gate sitting across it. This can easily compromise the
I-V if the oxide is charged, dirty or defective, as the MOS
action raises or lowers the surface "effective doping".
Damage can be simple charging short of outright failure,
from handling / probing and so on with inadequate ESD
controls, in-process charging (antenna), etc.