Its like you can pnly file accidents death or injury claim once you get injured.

MA is a "may issue" state, so they can refuse to allow you to defend yourself (gotta love socialism), but you can feel good knowing that they'll put the guy in jail after he injures or kills you.

Based on what project managers typically do, most full-time project managers would be classified as an employee, and that means you'd be responsible if they got injured (that's what worker's comp is for).

Is it in case you are injured yourself you would be able to go through their insurance?

Especially if you are in an environment where a child could get potentially injured. 

If the tenant causes a condition that results in someone getting injured and the they have Renters Insurance, there will be Liability coverage that the injured party can go after. 

The reason is that if I ever do anything stupid and seriously injure someone, the jury is going to be sympathetic to the victim.

What about if someone is injured, or worse, and cannot carry out their responsibilities.

i was injured at 16 ( of course I lied about my age to get the job so I wasnt exactly squeaky clean) by a guy smoking pot and drinking on the job. 

If someone injures themselves and sues, they will be suing the LLC and not you personally.