I have fixed skipped stitches because the threads are still there. I take a hand needle and thread it with the same thread. I then "make the stitch" by putting the needle beside the top thread, go down through to the back, over the bottom thread and bring the needle up to the top on the other side of the top stitch, I then tie the ends together to connect the top and bottom threads and then use my easy thread needle to bury the hand needle thread. I can do several pretend stitches by running the hand needle along inside the sandwich. Is it easy no, but I have done it.
For broken threads I would undo enough stitches until I had enough thread to tie and bury the ends. I would then continue the pattern on my sewing machine, knot the threads and bury the ends with my easy thread needles.