Healthy specimens grown in optimal conditions are mostly able to.
Pecan is a sun loving plant and leaves on branches must receive full sunlight to remain healthy. As trees get larger and branches begin to touch, the lower limbs receive less and less light and over time they die!
As a result, it is not uncommon for limbs to come"raining out" of these older native trees. All dropped limbs/branches are dead and are not too large in size (maybe 9" around at most).
Breakage is coming from the lowest limbs or lower 1/3 of the tree. Judging from the spring growth I see that the outer-most branches on the lowest limbs appear to be dead. (They were alive last year.) The tree is about 35' tall.
The root flare is not covered. Potential reasons for limb fall include: crop load,"breach" of the bark, wind, maybe drought, trapped bark,"shading out" and age.
The break was right in the middle of the branch, and there is no sign of insects, borers or decay.
Age itself does not necessarily make wood more prone to breakage. The strength of the wood is the same, but the stress and rigor from various outside forces are at play on the tree. Aug 21, Factors that can contribute to limb breakage in pecans (and sweetgums, too), are a heavy crop of pecans (or sweetgum fruit), lots of new spring growth from abundant rains, and very long limbs.
Crowded and older trees often have major limbs reaching out for more sunlight. Eventually, physics takes over and limbs break.
Aug 01, Pruning is usually best done in the fall, but dead wood and some interfering limbs can be pruned any time. Pecan tends to rip when cut so care must be used when cutting limbs so as to not damage the tree. Post some pictures of the tree and you might get a better response.
Best advice I can offer is stump grinding tweed heads you are not sure, hire someone.