Knitters and crocheters call that “plarn”. But I’ve not heard of anyone feeding it through a sewing machine first. We just roll up the strips. There’s a way to cut the bag so that it’s one long continuous strip.
A popular use for this material besides making reusable shopping bags is to make sleeping mats for homeless persons.
Edit: meant to say that I find the sewing machine use fascinating and will see if Google can shed more light on how to go about it and what machines it can/can’t be done with.