How to install reclaimed stone pathway without plastic edging?
You can dig down an inch or so and "plant" the stones without using a container as such. If you dig a 3 foot wide area and place the stone pieces in the excavated area, the pristine earth/grass surrounding them will pretty much hold them in place.
Your success will vary based on the soil type and amount of water involved, etc. Sandy soil that gets a lot of rain, for example may not work as well as other conditions.