That's gonna be quite the bill when the device does eventually disconnect...

I'd expect it to bill you for the extra data retroactively. (otherwise people would just save all the heavy downloads for the end of the month) I'd also expect it to calculate usage regularly as well as upon disconnect, so this plan wouldn't really work.

If this is really what you want to try though: take a rpi, open a Screen for a persistent terminal, run 'ping google.com' and disconnect from that screen (leaving it to endlessly ping google, at least until it's restarted).

Sounds like a way to get hit with a large bill when you finally disconnect. It would help to know what kind of monitoring or what service they are using. I would also check your contract to see if they prevent you from getting your own internet service. The whole thing sounds shady AF.

What happens when this device or whatever does eventually disconnect? No more data for the month, or get charged for it?

I'm kinda doing something similar with my phone. It's not supposed to be a hotspot, and I shouldn't have more than 20gb a month... But here I am on month four with 100gb of side loaded hotspot each month.

Just get an old wireless router that can also work as a WiFi extender/access point. Wireless routers have DNS and NTP functions so they consistently call out to servers for these functions, this way you can just connect to your modem which is forwarding the internet from your provider.

You should be able to find a used modem for cheap if you don't already have one spare.

It would be easy enough to have a raspberry pi always connected that just pings google.com or some other website every few seconds/minutes. I'm not sure that's your best solution or even what the best solution would be, but that would be very easy to set up.