One long continuous shot, sped-up until it becomes "live"
The answer above answers half of your question, and yes, it is trivial for anybody who has used a non-linear editor (NLE) such as Premiere Pro, Final Cut, Resolve, etc., to do speed ramp effects.  The film Koyaanisqatsi features many visual effects that include speeding up and slowing down time, which may help you better imagine the possibilities of the medium.  But NLEs are really only for off-line production.

To answer your second question about doing this while actually shooting, the short answer is no, nobody has built an off-the-shelf system for doing this.  The concept of "instant replay" (encompassed in a system such as the NewTek 3Play 425) illustrates how live feeds and recently (immediately) recorded clips can be used together while slowing down the playback rate.  And while it's theoretically possible to speed up playback rate (subject to available content in some buffer), it's not anything anybody has tried to do.  Instead, people edit offline and present a finished product after editing.