Bluetooth in background
Have an API for an application to interact with and listen for incomming connections from paired bluetooth devices while in background.
One possible use case:
A smart watch that uses the phone as a way to access information in the internet. For the most time the watch is disconnected from the phone, but from time to time it could connect to a service running on the phone (maybe timed, maybe because user presses a button on the phone) to send a request, which the service on the phone then handles (some additional data transfer between the phone and watch and the phone and some cloud service may be involved)
The actual trigger from device to phone could be done with Bluetooth LE if listening for incomming SPP connections is too much of a drain as long as it would be possible for an application to do some background processing and data transfer based on triggers comming from external hardware accessories.
Johannes Lappi commented
"(maybe timed, maybe because user presses a button on the phone)" should be button in the watch.