I'm not sure this is actually helpful. If the cryonics team isn't anywhere nearby having this information may very well translate close to "well, we're not getting that one." It would help but probably only in marginal cases. Still, could be potentially quite useful. There have been cases where a team has been on standby due to someone's ill health or is getting ready to go on standby and the person dies slightly earlier than expected. My impression is that in those cases they've generally still managed to preserve the patients fairly quickly. But we don't know how quick it needs to be. This could be the sort of thing where even small amounts of time could matter.
I'm not sure this is actually helpful. If the cryonics team isn't anywhere nearby having this information may very well translate close to "well, we're not getting that one."
Good thing there are telephones, ambulances and the possibility for neighbors or nearby friends to be emergency contacts. Add an enormously loud physical alarm to the device and anyone dying in their sleep who isn't living alone can have immediate attention of their housemates or family.
I'd expect such a system to occasionally save lives even apart from cryonic considerations and there would be a whole bunch of people who get chilled more rapidly.
Check out the latest episode of Castle (Headcase) to see Cryonics covered in mainstream fiction in a not entirely terrible manner. The details are not exactly accurate but probably not more inaccurate than similar fictionalised coverage of most other industries. In fact there is one obvious implementation difference that the company in Castle uses which is how things clearly ought to be:
Amulets of Immortality
It is not uncommon for cryonics enthusiasts to make 'immortality' jokes about their ALCOR necklaces but the equivalent on the show make the obvious practical next step. The patients have heart rate monitors with GPS signalers that signal the cryonics company as soon as the patient flatlines. This is just obviously the way things should be and it is regrettable that the market is not yet broad enough for 'obvious' to have been translated into common practice.
Other things to watch out for: