Convertible Rubber "Tubes"?

I was wondering the other way. My 1964 Valiant Conv has plastic grommets in holes in the raised area behind the back seat with such rubber hoses attached, but nowhere to connect them. Your photos shows what I expected - there are supposed to be drain fittings in the fabric "trunk liner". I have the trunk liner, but no such drains. It looks like the fabric was cut new by a shop for the prior owner so they never finished it. The trunk liner was uninstalled sitting in the trunk. I don't know that all cars had the trunk liner. I think its purpose is to catch water that drains off the top if you open and stow it while still wet.

My car also has the drip gutter which post #2 mentions. That is for water which leaks past the bottom of the top when the top is up. It drains down inside the body at the sides. Yes, cars are designed to flow water thru parts of the inside body, like what runs down the outside of the windows past the felt, and what runs into the cowl openings in front of the windshield flows down inside the rear of the front fenders. In cars with a sunroof, there is a drain tube at each corner underneath the moveable roof. You need to keep those drain openings clear of debris to minimize corrosion.