Stan, some are safer than others. Most of these cars are built nowadays with some sort of chassis modifications which would prevent the body from sliding off a VW pan like toppings off a pizza, but many are older -- and not built all that well.
Most owners try to make them as safe as they want them to be in order to drive them how they want to. The older cars, the pan-based ones -- are also the more under-powered ones with very little in the way of upgrades. They've been termed "starter cars," or "entry-level" here on the site for years.
Occasionally, some dummy will completely re-invent their car and post the results here for all to see. I might be such a dummy.
When I bought in, it was a very simple 80s-era pan car from Classic Motor Carriages for about $15K that hooked me. I utterly ignored maintenance for a few years, destroyed the mechanicals in the process and had to make a decision. I decided to keep it, but to make my own version of what I thought a fake Speedster should be. Instead of having a Volkswagen I could treat like crap, I had to do something better in order to justify the expense, so I enlisted the help of a fabricator and went to work.
After 18 months of fabrication and engineering work, we came up with a seriously rigid chassis and a 2.4-liter engine, better-than-average four-speed gearbox and a relatively visible answer to the low-slung "invisibility" problem -- orange powdercoat.
I've put thousands and thousands of miles on it, and as long as I'm able to keep my head on a swivel (and plan my turns), and there's only one Speedster in North America which might be able to keep up -- Rich Drewek's monster.
Depending on how insane you are, these cars can be turned into something really fun. I don't hesitate to get into the left lane, I'm able to punch it and outrun 911s. Like Danny P, I absolutely agree with the fun-meter for this general idea being linked to the sense of freedom you get from just being able to leave complications behind you.
Danny, incidentally, is the one guy I've actually run head-to-head with and watched his car disappear in front of me. His Spyder is amazing.