Yikes that looks like a homemade Star Dryvin copy using strips of something and a plain nail?
Anyway the standard procedure for 1/4" Star Dryvins is just treat them like buttonheads and use a 1/4" tuning fork below the hanger.
If you have 3/8" Star Dryvins, use a 1/4" tuning fork to pull just the nail (you can probably just use a claw hammer in many cases). Then pop out whatever you can of the sleeve (usually comes out with the hanger), and fish out the remaining steel sleeve shards. What's left is the lead sleeve - what you want to do for those is to screw in a 3/8" lag bolt on a hanger (lag bolts are cheap at any hardware store). Screw that in a couple full turns, then funk out the lead sleeve. This will bend the lag bolt, so bring enough lag bolts for however many 3/8" Star Dryvins you're going after (most 3/8" Star Dryvins are 2-2.5" long, but in soft rock you do see 3" long ones).