The tripod socket in my Century graphic fell out completely. The plastic around the socket has crumbled. Does anyone have an idea what can be done about this? I thought about screwing a metal plate with a tripod socket (I have one), but I doubt whether the plastic body will withstand the load and whether this will completely destroy it.

I'd try embedding your socket into the camera body with epoxy. That should create a permanent bond.

Already tried epoxy. As a result, it broke and the camera fell off the tripod. Luckily there were plastic boxes below...

You might try an auto body filler preparation such as Bondo. Note that any solution involving a glue or filler requires good surface preparation first - clean, grease-free and slightly rough surfaces. My usual surface prep for epoxy is to slightly roughen the surface with sandpaper or emery and de-grease it with methanol or rubbing alcohol.

The problem is that some of the plastic around the socket has split open and fallen apart. Therefore, it is difficult to talk about the surface there. There are very few points of contact left between the socket and the body. I'm still thinking about a metal plate, but I'm afraid of completely ruining the camera...

I think the camera has already been repaired with glue in the past. I didn't notice this when I bought it. It was hidden under the skin. But after 10-20 uses it collapsed..

Then I think you are looking at a metal plate. My approach would be to cut two identical metal plates, one for inside the body and the other for outside, out of aluminium or brass. Join them together with suitable machine screws running through the camera body, with the tripod socket sandwiched between them and held in place by soldering or gluing to one of the plates. One of the plates will have to have tapped holes for the machine screws. If you don’t have a suitable tap, you could use nuts instead, but there is a danger that they might project far enough inside to foul the bellows.

I already have such a ready-made plate with a soldered socket. I shot it with a large format wooden camera.