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.
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 cost is a central concern, then you might want to investigate a DIY route. Using a platform such as Arduino, you can purchase basic cameras, and using the Arduino board, trigger them together in a variety of ways...really only your imagination is your limit here. As most of these cameras are very small, it should be easy to pack them together.
I have linked to Adafruit for these items, but there are hundreds of vendors for Arduino or Raspberry Pi products.
This is the product recommended by Chris Breeze and Eric Pare at Xangle amongst others - the Esper Triggerbox https://www.esperhq.com/product/triggerbox/
The ESPER TriggerBox is the world’s leading programmable multi-camera shutter release controller. Up to 6 cameras can be connected to each TriggerBox and it allows multiple camera to be fired simultaneously or with programmed sequences and offsets + multiple TriggerBoxes can be linked together to synchronise larger multiple camera setups and they neatly stack together, a bit like LEGO bricks!
Breeze Systems makes software for controlling multiple cameras at once. It's worth looking at their site if only for inspiration.
Keep in mind that cheap cameras may not have a remote shutter release option; if this is for a one-time event, you might be better off renting a set of more capable cameras.
It can be done with GoPro cameras, and the GoPro wifi remote. You can pair one remote to multiple cameras, apparently you can control up to 50 cameras at once. See Controlling Multiple Cameras with One Wi-Fi Remote
Though it wouldn't be cheap, if you need to buy 50 of them. The cheapest current model would be the Hero3 White edition, which has wifi built in. Or you could use an older HD Hero or HD Hero 2 with the wifi bacpac, but these are now discontinued and getting harder to find.
This video is a nice example of using 52 GoPro cameras for a "bullet time" effect. https://www.youtube.com/watch?v=zKtAuflyc5w
The TriggerTrap mobile app allows configuration of master/slave modes which would do what you want - multiple slave triggers from one master.
Of course you'd still have to find a cheap phone and cable for each camera, so unless you have a ton of old android phones knocking around you're still paying a few $$ per camera to trigger them.
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