The grey squirrels in my UK garden routinely make what we call the 'leap of death' between two trees whose upper branches are a few feet apart, at different heights. I've seen two falls - one because the target branch snapped when the squirrel landed, the other during a high-speed chase where one of the squirrels apparently mis-jumped. In both cases the squirrels fell into lower level bushes and disappeared (no subsequent bodies). It's not unusual to see a squirrel with one one useless leg but still managing to feed and get around, so I can quite believe that they can recover from a broken limb given sufficient time.
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We also had a pheasant who routinely visited the garden and one day showed up with a broken leg, that survived for ages before eventually disappearing. Initially he sat quietly in the undergrowth but started hopping around and doing short flights (with clumsy landings). I put out bird seed for him and he incredibly quickly learned to hoot and flap outside my back door when he was hungry. He once followed me into my shed when he was expecting feeding and had to be shoo'd out.
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We also had a pheasant who routinely visited the garden and one day showed up with a broken leg, that survived for ages before eventually disappearing. Initially he sat quietly in the undergrowth but started hopping around and doing short flights (with clumsy landings). I put out bird seed for him and he incredibly quickly learned to hoot and flap outside my back door when he was hungry. He once followed me into my shed when he was expecting feeding and had to be shoo'd out.