While it is unlikely that anyone has been killed on account of excessive headspace, the implications of this are not something that should be dismissed out of hand.
The primary implication of an excess headspace condition is that the ctg case will expand (lengthen) to seal the chamber on firing. With a minor degree of excess this means nothing at all, except to the handloader who should then necksize in order to avoid excessive case working as a result of repeated case stretching and then compression in subsequent firing/resizing cycles. I once had a 7x57 Mauser with excessive headspace and managed the condition by neck sizing only after initial firing.
If headspace is sufficiently excessive, cases may stretch to the point where case separations can occur on firing resulting in the head portion of the case being extracted while the portion ahead of the separation remains lodged in the chamber. Apart from unreliability in a hunting situation, repeated case separations do admit hot propellant gases into the chamber which is not a good thing. In some cases there is no dramatic result, but in other cases gases can escape into the rifle and blow back into the shooter's face. Personally I would not fire a rifle where headspace was sufficiently excessive to cause repeated case separations. This is not an acceptable situation when you dealing with a 50,000 PSI pressure bloom a few inches in front of your face.
There are conventions on headspace with a min, max, and field measurement established for each ctg. It is an accepted norm that rifles where headspace in in excess of the "field" measurement, should be withdrawn from use until the situation is corrected. That was the arbitrary military rejection standard. Using the .30-06 as an example, the minimum, or "go" chamber length is 1.940. The maximum for newly rebarreled rifles, or "no-go" measurement, is 1.946, and the maximum or "field" measurement where rifles are withdrawn from service for overhaul is 1.950.
There is an interesting discussion of excessive headspace in Hatcher's Notebook where the author progressively reamed out the chamber of an M1917 Enfield to a measurement of 1.965 w/o encountering a case separation.

There is another variable here which can arise when a new bolt is swapped in. Should one lug not be bearing equally, what may initially appear to be a safe condition may change as the non-bearing lug is worn down to a point of full contact. Everyone is entitled to their own beliefs and tolerances on this topic, but if advising others, I would always urge staying within the established "field" measurement for a particular rifle-as determined by a headspace gauge.