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I see this post is a few days old, hopefully you check it.
First if the screen is off, how would they know where to touch and hold if such a thing could be done? I believe your request is flawed in that aspect at least slightly.
Second. If your plan is just to leave the device, I picture it hanging on the front of something like a doorbell next to a door or some kind of signage, and have people leave little clips of them saying whatever. There is a chance that this could be done by turning off the screen timeout, might be better if the device was set-up without a lock of any kind but many devices almost insist that a lock be set, and open the camera to video and just ask people to press the button to start and press it to end. Some devices will allow the screen not to timeout when charging and given that you intend to have the camera open for the whole time, however long that might be, you'd probably want to have it on charge anyway as the camera, +screen on, +extended time are going to mean going through a lot of battery life. Besides virtually everyone knows how to use a phone camera and with the front facing camera displayed this would allow them to make sure they are in frame while leaving the recording.
Another consideration would be storage. Again knowing very little about your intentions and based solely on what you've described, storage may become an issue. Just something to think about.
While I don't believe there are a lot of them I'm sure there are apps at the Play Store that will record by pushing a dummy app icon. They record without opening the camera and may even function the way you are requesting, hold to record release to stop, but again this requires the screen to be on and some way of indicating what should be done, etc etc etc...
I know this isn't the answer you were searching for however given the limited information provided and based on the conditions presented I feel this is a strong response and without personal experience with an app that I've actually used I don't see many other options.
What device do you have?
What OS is it running?
Is this an actually used everyday phone or just a spare or old phone just for this purpose?
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