The Avnei Nezer was asked about a person whose left arm had lost feeling and whether that person should continue to put tefillin on that arm. By comparison, a bird whose wing dries out is considered to be lacking that limb - would we say the same by a person, that the useless arm is considered to not even exist, or could the individual still put tefillin on given that the arm does physically exist?
The Avnei Nezer differentiates between birds and people on this point. He notes that by a bird, the wings are the main part of the animal (based on עוף יעופף), and that such a blemish would be considered a particularly catastrophic blemish, thus invalidating the animal. Such an injury by a human would not rise to this level.
Another consideration is whether putting tefillin on the right arm would be considered better than putting them on the damaged left arm. The Avnei Nezer feels that since the left arm still exists, there is no reason to place the tefillin on the right (wrong) arm.