Why Can't You Keep A Tree That Has Died?
If you bought your house because of those gorgeous trees out back, the news that one of them has finally died is very sad. The usual advice for dealing with dead trees is to remove them, but if the tree still looks interesting or protects your home from afternoon sunlight, the idea of removing it might not be your favourite. If a tree is dead but still looking generally tree-like, why can't you keep it? Basically, you can't see what's happening inside the tree, and whatever is going on in there can appear externally and so suddenly that you might not have adequate time to respond before adjacent trees — or worse, your home — end up suffering.
Dead Trees Fall Eventually
Here's the most dangerous issue: Dead trees fall eventually. It could take years, of course, but the problem is that you don't know. You absolutely don't know, and you don't want to find that a wind storm has finally caused the tree to keel over. Especially if your house is close to it.
When you know that the tree is dead, removing it is the best way to ensure your safety from that falling tree. And even if your house isn't near it, other structures and other people's property could suffer if it falls. Then you'd have a potential lawsuit on your hands. It's easier to arrange for a tree service to remove the tree.
And Then There Are the Pests That Move In
As dead trees sit, they can rot from the inside and give pests and pathogens a home. Destructive bugs may take up residence, fungi can grow, and diseases can spread from the dead tree to nearby live trees. While it's understandable that you'd want to keep the tree so that it continued to provide shade, you're better off removing the dead tree and having a live, fast-growing tree planted in its place.
The Stump Could Be Preserved
If this is a particularly sentimental tree and you're not concerned about having a fully grown tree there because of light and shade issues, you might look into preserving the stump of the tree. You'll need a tree service to evaluate the stump once the tree has been cut down; for example, a stump that shows signs of rot should be removed, chopped up and discarded. But a generally "healthy" (albeit dead) stump could be removed from the spot and treated as a large piece of timber, eventually being preserved as something like a garden bench.
Call in a tree removal service to look at the tree and arrange for its removal. If you want to keep the stump, ask about having it removed but left behind so you can see what you want to turn it into.