This is written after two different users of generators suffered damage to equipment when generator sets were connected as an alternative supply, but did not connect the Neutral to the Earthing system.
Please note that we are not going to cover another fault that happens when connecting gen-sets as an alternative supply being the accidental swapping of a Live and Neutral e.g. A-B-C-N is swapped and connected as N-C-B-A which causes two of the phases to be subjected to 400V instead of 230V.
Let's first differentiate between a floating Neutral and a loose Neutral. A loose Neutral is where there is no solid connection between the star-point of the supply and the star-point of the load. Please note we said 'not solid', and not "disconnected". 'Not solid' or 'loose' means any Neutral that is not bonded with at least 2x phase and through this can lead to imbalance on the load side.
A floating Neutral (star-point not bonded to Earth) is actually a floating supply i.e. the whole supply can, as an entity, float from Earth. But we need to cover one very important fact first.
Neutral can no longer be called Neutral! The term is given to this current carrying conductor through it being 'neutralised' with Earth (and finally Ground). As it can no longer hold on to Earth, it can no longer hold on to the name usually given it. We therefore have to revert to the place where this conductor is connected, this being the star-point of the transformer - and we call it such.
There are two inherent 'dangers' with floating systems, although neither 'danger' damages equipment operating on the floating supply. As is, ships have used this form of supply system very successfully for quite some time now! But first,...
On 3-phase systems there is a tendency for the star-point and Phases to want to 'balance out' based on the ratio of leakage on each Phase to Earth. The star-point will remain close to 0V depending on the distribution of the load and subsequent leakage (higher load on a phase usually means higher leakage).
If the supply is single phase then it is not uncommon to find the two current carrying conductors balancing out at about half-supply voltage each (on 230V this would mean 125V on both). Investigating leakage currents will show that, if anything, a floating supply significantly reduces leakage currents and therefore minimises damage to equipment through leakage via signal cables.
On to the 'dangers'.
The first 'danger' is; Should a Live-Earth fault occur then it is highly likely that NO protection will trip as there is no return for the fault currents. The star-point will no longer be 0V and will now rise to 230V. The second 'danger' is now present as only on a second fault will any protection operate. This danger increases with 3-phase in that a Phase-Earth fault will cause not only the star-point to rise to 230V, but the other phases will now reach 400V. Should the second fault occur then this will occur at the said 400V rather than the 'designed for' 230V.
Equipment designed for 230V can usually withstand the 400V from Phase to Earth without the danger of flash-over (note, not 'Phase-Neutral' which still remains 230V). It may stress the insulation a little, but nothing is likely to come of it (modern design specifications ensure that desigers are aware of what's required).
Based on the above, it is safe to say that a floating 'Neutral' is not the common cause of the equipment failure. Such damage is more attributable to the fact that gen-sets are not clean sources of energy, and it was probably one of a range of factors from high peak voltages to just simple overvoltage or something similar. Or, simply, that someone forgot to connect the Neutral......