Answer: The symptoms sound suspiciously like those of Gray Mold, a fungal disease. The disease usually appears first on necks near the soil line, then involves the entire bulbs by the time they're mature. The fungus then moves up into the succulent leaves. It's difficult to control, especially in wet soils, which allows the fungal spores to spread to other bulbs.
Remove and destroy in infected garlic and don't plant garlic or onions in that same garden site. Crop rotation is extremely important to avoid repeating problems like the one you describe.
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