If there’s currently only a single fireplace in the house, the second flue might have been installed as an option for additional fireplace, heating stove, or other appliance installation in the future.
It could also serve a fireplace or other appliance (natural draft water heater, heating furnace / boiler, etc.) that has been removed and this area sealed off completely so it’s not visible anymore, or replaced with a high efficiency appliance utilizing different types of venting instead of a chimney.
I’d highly recommend a rain cap and screen for both flues (remove plate), even if one of them is not in use any more. Check this Q&A for my answer I gave Chris - seal unused chimney
The difference in your case would be that you don’t know what (if anything) they did at the base of that second flue. Maybe you can look inside that flue from the top and see what they did at the bottom, or look for a cleanout at the chimney’s base and use a mirror to check what’s above it. Depending on the flue’s shape you may or may not be able to view its interior.
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