Question: I want to assemble several cameras, triggered by a single remote. Is this possible?
The trigger doesn't have to be wireless, because the cameras will be very near to each other. The cameras need to be very cheap, because I'll be needing 50 of them.

Answer: 
I think there is one main problem with what you are asking : a cheap camera probably won't come with an external triggering system.

So you could :

* buy a bunch of (not so) cheap cameras (~$100 ?) with an external trigger socket, and for the trigger go the cheaper way : buy the hardware and build it yourself. You need plugs compatible with the (possibly model-specific) sockets, connect them all in parallel with some wires to a single pushbutton (you also need the schematic of the plug to know how to connect...).
* buy a bunch of very cheap cameras (~$40-50) without an external trigger and "hack" them : remove the trigger button and solder/attach wires instead, and connect them to a single pushbutton like above.

Actually it may require a "two-level" pushbutton like the original one (actually a double sided temporary flip switch, or two distinct pushbuttons, or...) in order to prefocus, then take the shots.

If the camera model is the same, I don't foresee a problem with connecting all the triggers in parallel. Otherwise some electronics might become necessary (relays/optocouplers/...).

And as a final note : beware that with cheap cameras you'll get... your money's worth : fewer control options, good image quality in good lighting conditions but otherwise "maybe not", etc.
If you want to go the low cost route Mike's Cool Stuff shows a design for doing this. It is fairly complex and requires detailed elecronics knowledge to create. He avoids using costly modules such as wifi, uses low cost camera modules and tackles subtle issues such as power drain, sequence triggers etc. <https://m.youtube.com/watch?v=Lvyslu65V3s>