I have been using the basic purl bind off. The last cast looks like it is going to fall out.I am a new knitter so I am not sure how it should look.
You need to cut the yarn a few inches away from the last stitch/loop and pull the loop. Or pull the tail (end of yarn) through the loop. Then take the tail and thread it through the nearby stitches to anchor it. If you just leave, the tail could get pulled and unravel it all.