ENTROPY

At one time, these woodpecker condos were occupied by Red-headed Woodpeckers (Melanerpes erythrocephalus). You physics majors out there will recognize entropy in progress.  It happens slowly, most of the time, but it always happens unless there's a constant input of energy into the system.
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For you non-physics majors, the concept of entropy is typically defined as:  "...entropy, the measure of a system's thermal energy per unit temperature that is unavailable for doing useful work. Because work is obtained from ordered molecular motion, the amount of entropy is also a measure of the molecular disorder, or randomness, of a system."  (Wiki)
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That boils down to...no energy input, things fall apart.  Have you noticed that unless you constantly clean up a room in your home or at work (energy input) it tends to descend into disorder?  Entropy!
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Since photosynthesis is no longer occurring in this dead limb, there is no energy input and therefore it begins to decay...with the help of decomposer organisms, and will, ultimately, return to the soil from whence it came, only to be recycled and used again as nutrients by a growing plant.
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Thus endeth the lesson in Physics 101.   Best in Large.