As several have noted above, a slowly dying tree is as bad as a growing one. It isn't just the top part you affect- it's also roots which can be heaving your foundation up, or will cause a cave in when gone. As a tree dies, it can drop limbs - or rather branches. Roundup brush killer and salt are both used to kill stumps by applying into drilled holes. Roundup stays in the ground so care must be taken. You didn't indicate the size of the tree, but removal of smaller limbs can damage rooftops just as limb drop can. So, costs must be evaluated in case of worst case scenarios. Good luck
