Until 4/1998 the door liner was a plastic sheet that fitted either door — 51488397163. After that a molded rigid foam liner was used — 51488410037 left and 51488410038 right. The rigid foam liners are called "insulation", so sound deadening must have been their improvement. Both types of liners are adhered to the door by round 5/16” diameter butyl window sealing tape.
The door liners ensure that any water that enters the door by dropping down past the felt/rubber seal from the outside of the raised window, stays in the door. Water in the door goes out the door drains to the outside of the door sill and out of the car.
If the door liner was not there, water entering past the upper felt/rubber seal from the outside of the raised window, would drip and splash on the back of the door panel, run down the back of the panel and escape the interior of the door. The water would emerge from under the door panel, run down over the inner door sill, and into the footwell.
At the bottom and sides of the liner, the butyl tape is a critical seal that keeps water inside the door instead of coming out under the door panel.
The butyl tape is used at the top edge of the plastic liner to hang the floppy sheet in place while the sides and bottom are pressed into the rest of the tape. Since the rigid liner is self-supporting, the tape at the top was omitted.
Here's my plastic liner taped up for greasing the window sliders:
Note also that higher up inside the doors, the interior door handles have rigid foam covers stuck to the door with butyl tape, to keep water from getting on the door panel from the handles' holes in the metal. The slots are for the actuator rods to pass out of the covers.
A few days later...
I opened up my passenger door to lube its sliders. Its foam handle cover had fallen off like on the driver door. The adhesive looks like it came from a tube and was not applied in the right places. I will replace both covers using round butyl tape pressed firmly. I also ordered the newer rigid foam door liners to replace my flimsy plastic sheet liners.