There are quite a few coccoids - homopterans: bugs related to aphids.
Scale insect - Wikipedia, the free encyclopedia
The large ones producing 'cotton wool' are likely to be
Pulvinaria regalis the horse chestnut scale although I've never seen that on holly. That is not at all host-specific although many others are.
Like all homopteran bugs they live by sucking sap from plants. They can be very damaging. Citrus crops in particular suffer from three or four species.
They're quite peculiar, the males are very small and have no scales - they mate and disappear. Classically the females live in the soil over winter (or summer if it's that sort of climate) then climb up trees or other plants to feed and grow. The large final scales, as you say, are dead females which have returned down the tree to lay their eggs and die - the eggs and young are then protected by the scale and, in some cases, the 'cotton wool' or other exudates.
They are not easily attacked by predators although chilocorine ladybirds (such as the pine ladybird) specialise on them. Notably, the very first
successful use of an insect to biologically control a pest was
Rodolia cardinalis first used over a century ago to control a scale
Icerya purchasi
Vedalia beetle - Rodolia cardinalis - Wildlife Photography