I can't answer your question because, reading grammatically, you asked about a lawsuit against an injury to a company. What that means is that the company was injured (presumably financially). Then you ask if it would change anything if there were a lawsuit - change what? Change the minds of those in charge of the company?
My best guess as to what you are asking is: "If there were a potential lawsuit against a company for a work related injury, would it hurt my case (my lawsuit) if I wrote a letter to the company and explained to them the pain that they caused me? Would the company be more willing to settle or apologize or take some other action to make amends if I filed a lawsuit?"
If that is your question, such a letter should be carefully crafted by someone who writes well. The purpose of the letter is tricky and you should probably seek legal counsel before writing such a letter so you don't harm any potential lawsuit you may have. Whether a company would be more willing to settle if they were facing a suit, is hard to say. They would be forced to deal with the situation if they were served with a lawsuit. Usually, when people are forced into doing things, they are quite resentful. If they are spoken to reasonably, sometimes negotiations can be successful. You really ought to talk to a lawyer. I don't know a decent lawyer who would charge you to talk to you briefly over the phone to find out whether it's worth their time to have you come in for an office appointment. They will make a preliminary decision as to whether you have a case with any merit over the phone. If they ask you to come in to the office for an appointment, then you would ask about fees. But, by the time you got off the phone, you would have a really good idea as to whether you should attempt to negotiate with the company or file suit or just accept your injuries and move on with your life. If you contributed to or caused your own injuries, that is the sort of case that would result in you possibly having to just accept the injuries and move on.
Map, Directions, Telephone Number(s)
Family Criminal Law Division Chief
District Attorney's Office
1201 Franklin, 2nd Fl.
Houston, TX 77002
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