I'm not saying it couldn't be done, but it would be very difficult to do in a way that wouldn't be noticed, especially once it became common knowledge.
No mugger is going to stick around longer than they have to. The need to get away quickly would dictate the design choices for such functionality. Maybe we'll get lucky and a few security developers at Apple/Google/etc. will read this discussion and get some good ideas to think about :).
I'm not affiliated with Cerberus in any way, just a happy customer.
[1] https://play.google.com/store/apps/details?id=com.lsdroid.ce...
If the thieves are somewhat savvy they will just hold down the power button until it turns off. Can't disable that in software.
You know what would be the better thing to do in that situation? Make damn sure shit works and they get what they're looking for. I'll worry about cancelling credit cards, etc. later.
For post-contact response, maybe even an IVR system you can call (from a public phone or something) and give an audio or DTMF password.
(I'd also like to get my phone droned after I move out of danger close radius, or the civilized city equivalent (police/bike gang/etc. show up at geolocation))
You could force the device to self-wipe data storage after X minutes or force specific apps to 'crash' on open (email, 2FA apps, banking, etc.) where even offline access could be detrimental.
When assaulted, just cooperate.
Given that use this tactic will probably increase over time, phones and other portable computers should really support duress passwords.
The device should look like it unlocked properly, but really put everything in a type of read-only mode where writes and certain network transactions return success but don't actually do anything. Obviously, if network access (any type) is available, some sort of silent alarm can be raised at the same time.