My guess is the branches aren't really supporting it. My guess is the tree is resting on the canopy and the broken trunk. When the trunk is completely severed, it may unpredictably twist and fall to one side or the other. Whichever way it twists, it looks like the severed butt end will still fall on your fence.
To explain, it looks unpredictable whether the tree will fall to the left or to the right when severed. One limb is already resting on your fence. What I think is predictable is that when severed, the butt end is going to want to spring out towards your property and fall in an arc even further onto your fence.
Also looks like maybe 1/3 of the splintered trunk is holding the tree up with a lot of weight of the trunk exerting leverage on the splintered hinge.
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