If you bear in mind that anything can happen in the transistion area (1, 0, both, not really either) then you might think that is not really acceptable.
What happens if the analog signal is at 4V, but the input max voltage is 3V
You destroy the device. Another posssibility is that the source of the analog signal can't really cope with being able to supply the required current, but this is more likely to cause malfunction of the source circuit (or no effect) than damage to the source.
Also, will the negative part just get clipped, and/or will it cause any other problems.
Yes.
If the source can suppply enough current, it will damage the fpga. Maybe it can't, and in this case the signal will be clipped. Maybe the source will be damaged, although this is less likely with typical sources.