I would not keep any device with a fully exhausted battery just because a battery in a good working condition can already be a fire hazard. So, a depleted one who knows how it can reacts? I would properly dispose of it by recycling it.
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I used to have an old phone like that next to my PC keyboard to start macro's: Macro Deck (open source code here).
It is never secure or truly safe to use. The kernel cannot be updated and so all vulnerabilities are adding up. You're giving out enough info to figure out what device you are using just in the fingerprinting with every online connection. It is relatively easy for someone to look for you and exploit a known vulnerability. They don't need a zero day or any kind of exploit. You device likely has the last secure kernel on it and there will be many published critical vulnerabilities that can be scripted.
Even if you stay offline and do not use WiFi or use airplane mode, you're not able to verify what the modem is doing in the real world. You never owned the thing in the first place and the reason why is the proprietary binary module that supports the system on chip and modem.
All that said, it is no different than something like an old computer running Windows XT or with CP/M.
Hmm... Thing is, GrapheneOS is already more secure than stock Android, and the hardened memory allocator, spoofed MAC address, unprivileged Play Services, and much more as example, strongly help to reduce attack surface.
I think just going online, like connecting to my home router and doing system updates, won't strongly compromise security.
Only real use ive found for an old android phone was using it as a backup alarm clock. Surprisingly kind of hard to find alarm clocks that are as good as ones on a phone.
Another good use could be gaming handheld for emulators.
Emergency backup phone thats charged up in your car? Idk dude with the way phones are locked down and the difference across them, hard to really have any use afted security updates end uness you wanna patch your own kernal.
You can run servers on Android as well. Kodi is a dedicated media server app for streaming and the like, which is available for Android as well. It might also be an interesting interface for Home Assistant, if you are into that kind of stuff. As in put it on a stand or something permanently plugged in. Something like an old school radio might also be an idea. As in connect it to some good loud speakers and just play music from it.
If the device doesn't need to be portable removing the battery could improve safety a bit (and bypass some issues from the damaged USB port).
It looks like it's possible to connect an external power source where the battery normally links up https://www.reddit.com/r/GooglePixel/comments/18404z7/run_pixel_3_without_battery/
Not sure if that's helpful but it might make turning the phone into a reliable embedded device easier?
While I generally disapprove of resin printing, this seems like a good use case for building a Lumibee. They're open source resin printers that run off old cellphones.
Trail camera.
I've heard some people use Termux to self-host some Linux services on an old phone. I'm not sure though if that's feasible with a dead battery and a damaged USB port...