Encryption and public keys. That problem has been solved for a long time, it just needs to be adapted for data granularity so that each service can be exposed to specific bits of data and actions that modify them within constraints.

The data lives on your machine, or in a pod controlled by you. This data would be "live" as long as the you like by continually updating encrypted values that are only decrypted using each service's public key. If you want to cut off access to the data, turn off the hose. From there, you'll need to rely on your local government if you require the service to purge existing data, but that's nothing new. I've described in great depth on this website before what such a system might look like. Only public keys and encrypted data are passed around.

Tim Berners-Lee is also tackling this problem with Solid.