A boiled egg can last in the fridge for up to 7 days if stored properly, whether it is peeled or unpeeled. It is best to keep unpeeled eggs in their shells until ready to eat, as the shell helps protect the egg from bacteria and prevents odor absorption. Peeled eggs should be kept in an airtight container, possibly with a damp paper towel or submerged in fresh water changed daily to maintain moisture. Boiled eggs should be refrigerated within two hours of cooking and should not be left out at room temperature for more than 2 hours to prevent bacterial growth. Signs of spoilage include a sulfuric smell or off taste, and spoiled eggs should be discarded safely.