Hey that really sucks. What section of your trap tore? Was it the upper, middle, or lower? I have a complete tear in my lower trap and don't know what to do. What has your orthopedic surgeon said about what he/she thinks you should do? Surgery?
By the way to answer your question, it is VERY VERY rare to have a completely torn trap. As far as other treatment options you have, you can see a M.A.T therapist. They will get your other muscles that are in the area to work at peak capacity so they will pick up the slack that the trap is no longer doing. You could also skip the surgery and just go straight to physical therapy. They will make sure that all your surrounding muscles are very strong so they will pick up the slack of your trap. But I would suggest you go see the surgeon first and git his/her take on what they think you should do and what all your options are. But for now, do not workout at all, take it really easy on your shoulder, ice it and then apply heat. Also you can take fish oil to help reduce the inflammation. I hope it all goes well for you. Also considering we both have the same injury and considering how rare it is, if you'd like I can give you my email and maybe I can help give you some advice and visa versa. Well either way good luck and know that there is someone else out there who is going through pretty much the same thing that you are, hopefully that will make you not feel like you're the only one. Good luck,
Kevin