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It's likely that the trunk was already dying before woodpeckers started hunting for grubs in the rotten wood. But yes, apple trees do sprout from lower down as you describe - sometimes they throw out a lot of slim whippy bushy branches, or sometimes 'proper' new branches start growing lower down. The latter may rejuvenate the tree, but in my experience the former will rarely grow into good fruiting branches.
However, a venerable apple tree is a thing of beauty and of immense value to wildlife, harbouring as it will all sorts of bugs and insects. If you can find berries from a misletoe that came from an apple tree you might be able to grow some on your parents' Bramley, and it would look wonderful with a rambling rose such as Rambling Rector growing up and through it's branches, or even a clematis.
If your parents decide to take the top off the tree it would be really good to put the trunk somewhere in the garden and leave it to rot down naturally, providing invaluable habitat for all sorts of wildlife. http://gardenofeaden.blogspot.co.uk/2008/12/importance-of-log-piles-to-native.html
I would love to have a really old apple tree in this garden, like the ones in the old orchard on the farm where I was a child. You and your parents really are very lucky I'm glad you are going to continue to enjoy it.