The basic answer is no -- once captured, the picture is the picture, and there is nothing you can do to recover information that you never recorded (such as a person's face, if all you captured was blur).
There are some cameras that can do this trickery, but they generally have severe drawbacks of their own, such as drastically less resolution.
OTOH, small-sensor, cheapo cameras (like phone cameras) can do it, by capturing everything in focus, and then selectively blurring parts of the image in post, using software. This would allow you to change which parts are blurred after the fact. However they are basically guessing about which parts of the image are at what distance, and will generally do an inaccurate, sloppy job. In any case, for these types of systems, the original image has to be all in focus.
There may be AI tools which allow you to un-blur bits of your image after the fact; but they're basically just guessing. Be prepared for hilarious results.
