The solution is to taper the lining slightly so it fits better inside the bag or basket. Quick, simple and you’ll have a more polished project once it’s completed.
Another issue that sometimes crops up, and not just with bags and boxes, is that the open edges of a turned project don’t always fold nicely inside. It can be hard to make that opening look just like the seam on either side when the edges don’t want to turn under neatly.
There’s also an easy solution for that. Simply turn 90 degrees and sew straight to the outside edge on either side of the space you’re leaving open for turning. (Once the project is turned and the edges of the opening pressed into place, use this hand stitch to close the opening.)
Both solutions are explained in an article by Chris from Made by ChrissieD. Neither solution takes much extra time and both will produce nicer finishes, whether for linings or for projects that are turned.