1- If he carries on driving like that, he'll end up dead. (https://www.macmillandictionary.com/us/dictionary/american/end-up)
2- The last time he was in the room with a serial killer, he ended up chained to a hospital bed.
(It is from a tv-series. He was in a room with a serial killer as a result he had a panic attack then in the hospital they chained him to a bed because he was still having some episodes after the incident.)
Is using "being" before the adjective/past participle here optional?
1a- If he carries on driving like that, he'll end up being dead.
2a- The last time he was in the room with a serial killer, he ended up being chained to a hospital bed
" I'm not among them. I find it awkward sounding. It isn't really wrong.
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Many people are fine with that use of "being." I'm not among them. I find it awkward sounding. It isn't really wrong. It sounds much better without "being."