How do you stop a dog from digging under the fence (chainlink and privacy)?

He is fixed and gets plenty of attention and exercise. He is a rescued dog that we have had for about 2 months. We were told he was between 1 and 2 years old. Because of many behaviors, I think he is closer to 1. He began escaping from the start through holes the neighbor's dog dug into our yard (forgot about them). When I plugged those up, he just started digging new ones. After chasing him down a few times, I just put him on a line. I hate doing that when our older dog does not need one. I have seen the suggestion of mothballs. Do you just set them out along the fence line or do you bury them a little? Thanks!!