When you get fresh snow it can have very large air pockets within the fall. Size of flake, moisture levels etc all impact on this. If you’ve skied off piste you’ll know that as fresh powder fall tends to be lighter and you cut through it easily. If however the wind has been blowing, this can compact more and be denser and much harder to ski through. As snow settles it does tend to compact, so day old powder feel different to stuff that has been lying, or indeed compacted by skiing. but it will depend on lots of factors. You will ski on top of snow eventually and not through it. IYSWIM.
This is the base that new snow falls onto. If there has been little snow and the snow has warmed (possibly) or it has turned to ice. The new snow may not bond well with the base layer. If there is a lot of snow this is heavy, but it may not have ‘stuck’ to the layer below. Nothing is helping this process and sometimes the grip of this new snow is poor and it will slide off, creating an avalanche. High risk areas being those where gravity is playing a bigger part!
On the piste the bashers come and churn the layers together and this knits the various snowfalls together. They churn it (importantly), move it around, apply weight and smooth it out. It compacts the base and creates ice at the bottom which acts as a fridge, but it is softer on the top, but it is a progression (ideally) that means it is a firm and stable layer. Not layer on layer but a churned icecream.
The lack of base is also why some pistes remain shut. They need enough snow to begin packing it down and creating an adhered base. When new snow sits on too thin a base, particularly when steep, it doesn’t grip in the same way. I would never go down a closed run for this reason, they don’t shut stuff unless there is good reason – this is how a few kids died a couple of years ago
Clearly what I’ve written above is the worst case, slippery ice with new light snow, but you see how the piste and the off piste conditions will be very different. I would reassure your daughter. I don’t know this for a fact, but I’ve never heard of an avalanche on piste.