Claiming O:
It’s a good question, I too would like to know. What kind of construction is this grammatically speaking?
Analysis
I’m trying to spend more of my time on things I don’t understand as opposed to detailing things I understand fairly well.
Vocabulary:
この人の生死…
✩生死 is new to me and therefore comment worthy. According to my dictionary, is a noun meaning ‘life and death’. It can also mean samsara and death in Buddhist terminology but I don’t think it applies here.
僕は握っている
✩握る is, you guessed it, the new vocabulary for me. It means ‘‘to grasp’’. It’s in the progressive form (non-finite form)/
Interpretation
Well the right part means ‘This person’s life and death’ while the left part means I’m holding it…
So:
この人の生死僕は握っている
The life and death of that person is my hands. (tweaked to sound good in English)
or
I’m holding the life and death of that person in my hands