I can't think about a particular name for this technique it's a kind of feedback loop trick but kept under control & applied to a portion of the audio going through the reverb at the point you decide to "freeze" it. Not all reverb plug-ins have a "freeze" feature, one of the most famous reverb to achieve this trick is "BlackHole" from Enventide Audio. It has got 2 modes for the feedback which are "infinite" and "freeze" and that's the 2nd one which is interesting to achieve this effect, if you use the "infinite" mode the feedback will simply add to itself and build up over & over and it can quickly get out of control and create a very loud and "nasty" sound, like the kind of feedback you can have with a mic and a speaker when monitoring the signal in.
So just something to be aware of and it will be more easy to achieve with a reverb that's got a proper "freeze" function. If you don't have the option, you can try to increase the feedback manually and stop it before it gets out of hand. If you record this to another audio track you can then work with the audio and make a loop with it or further process it to your needs.
There's a lot you can do by recording reverb, delays and other effects to audio : Eq or filter them, reverse them, send them to other effects, it's a good way to be creative and to achieve some interesting & unique sound design.
Last point is that ultimately you could create the feedback loop with any reverb plugin by setting some I/O routing : so your audio source is sent to a reverb on a return track, the reverb from that return is sent to the input of a new audio track and the output of this audio track is sent again to the reverb creating the feedback loop.
Same rule applies : be careful as the feedback will build up and don't turn that 2nd send knob to the max, your ears, monitors or headphones are not gonna like it
Hope this helps