The large scaffold limb on the right side of this tree ends abruptly near the residence. It may have broken during a previous storm, or it may have been intentionally shortened with a heading cut. That cannot be confirmed from this photograph alone.  
Either condition deserves an on-site inspection before someone makes another cut.  
The end of the limb should be evaluated for torn wood, cracks, cavities, decay, loose material, wound response, and evidence of previous pruning. The remaining lateral branch, its attachment, and the amount of weight extending toward the house should also be assessed.  
Depending on those findings, the appropriate prescription might involve removing unstable material at the proper pruning point, reducing the limb to a suitable lateral, beginning staged restoration pruning, or removing the entire limb if its condition and the consequences of possible failure justify it.  
The important point is that simply cutting the limb shorter again may create another problem.  
A heading cut removes a branch at an arbitrary location or cuts it back to a lateral that is too small to assume the terminal role. On a mature shade tree, that can leave a stub that closes poorly and may stimulate clusters of vigorous sprouts near the cut. As those sprouts grow, their attachments can become another structural and maintenance concern.  
The nearby house increases the potential consequences of failure, but proximity alone does not prove that the limb is likely to fail or that complete removal is necessary.  
This is why the objective should be established before pruning begins. Inspect first, determine the defect and target, and then develop a pruning prescription based on the actual condition of the tree.

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*Disclosure: I am a consulting arborist in coastal Alabama. This post is educational and is not intended to diagnose the tree from a photograph.*

When a large limb ends abruptly near a house: broken limb or old heading cut?