When you refer to the "port plug" are you referencing the Fill Hole plug that is normally the color of the ink cart you are filling OR the orange plug that covers the air vent hole?
The only plug that needs be reinstalled is the Fill hole plug, located at the rear of the cartridge, where you inject the ink into the cartridge. The orange plug needs to remain removed from the cartridge so when installed into the printer the air is allowed to flow through the inlet port. If you left the Fill hole plug out, the cartridge would leak ink out when tipped back to it's original position and installed in the printer. But not internally, but rather out the back of the cartridge instead. You would have an inky mess all over the front of the printer itself, you would certainly see this.
I've personally never experienced a 3880 draining a cartridge of ink, but as Brian mentioned there is evidence of other users experiencing this bizarre behavior due to ink selector defects internally. This is a possibility, that we shouldn't rule out.
As Jeff mentioned, your capping station is probably filled with ink, from the the internal wick of ink. I don't believe this was/is caused by the cartridge having a defect. The Cartridge supplies ink into internal ink lines, which run into dampers aka. Ink Selector unit. This ink selector unit OR damper assembly would have to in the open position due to a defect within the printer itself. I see you have 2 other position cartridges of ours, have you installed those with success?
This ink probably wicked into the capping station, then into your waste tank, at this point that would have been 80mls of ink, which the printer would not have monitored as part of any ink waste accumulation.
If your printer is still fairly new, I would contact Epson for warranty replacement.
As I said, this is NOT a normal behavior for this printer and these cartridge models due to the ink system inside the printer. Once the ink reaches the dampers (aka. the ink selector unit) the ink physically stops at the damper unless it's called for and the damper opens. You can think of these dampers as one way valves, when they are shut/closed the ink is stopped from going anywhere. When they are open the ink is flowing through the head and either onto the media or into the capping station, then to the waste tank.
For good measure I am sending you a replacement cartridge, as I said I would be surprised if it fixes the problem, but anything is possible. Please let me know how it turns out.