A friend of mine told me Pianoteq was always recording the MIDI in the background.
It would be a cool feature for people who suddenly realize they forgot to click the record button, or just have a good idea when improvising before recording.
Thanks foxAsteria! I didn't know what keywords to search!
It looks that this feature request is quite old... Do somebody know if another DAW has this function? If it was Reaper-exclusive, I'm sure a lot of hesitating people would join us.
Digital Performer, Tracktion, Cubase, Studio One, Pro Tools, Samplitude/Sequoia, Fruity Loops, Logic, maybe some others as well. It seems to be more common as a MIDI-only feature.