Tommy Flanagan had some severe facial scarring following an accident, and he still gets work (Gladiator was the first movie I saw him in).
Aw, bummer. I saw this thread title and immediately thought of Richard Lynch, who was one of my favorite actors in the late '70s and early '80s. He was great in the TV movie “Vampire,” BTW. I thought he was obscure enough that I might get to answer this one before somebody else did, but it appears I’ve underestimated the Dope. 
Thanks for reminding me of him!
Wouldn’t it be cool if they could get him and Rutger to play brothers in something. While they’re at it, they could get Owen Wilson and Johnny Fairplay from Survivor to play another pair of brothers. Maybe they could redo The Long Riders.
Parminder Nagra fits the bill as well. The burn on her leg seen in Beckham is real.
Who’s the (very) burn-scarred actor in 633 Squadron?
James Stacy stayed in acting, up to the early 90’s, after a motorcycle accident caused the amputation of an arm and a leg. I always thought he was cute in the old Western “Lancer” on TV.
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Sort of a hijack -
Who are some other actors that had facial injuries
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There’s Montgomery Clift, whose gorgeous features made him a heartthrob until his 1956 car accident (in which most of his facial bones were broken). He was unscarred but his facial structure was somewhat altered from what had been near pretty-boy perfection. (Still pretty handsome, IMHO.)
He’d been troubled before, but after the accident he spiraled into depression and substance abuse, until finally his bad habits caught up with him when he died in 1966.
Sad story. But he still did some amazing work in those post-accident years, especially in Judgement at Nuremburg as a mentally slow man victimized by the Nazi racial purification laws.
Wow, I went through his IMDB resume, and I have seen exactly one of the films that guy made, and that film I scarcely remember (one of the first few he made, and it’s a very bit, unnamed part). I have seen a lot of the TV shows he was in but no way I’d remember this guy. He’s been in some really forgettable stuff. I’m impressed anyone knows who he is.
In my case, his face is very rememberable. Just not his name. 