From the wording of your post I'm assuming you are the client rather than a nail tech?
Please, please don't rip your nail enhancements off if they lift, you will be causing untold damage to your natural nail plate underneath! (As you have already discovered!)
I would advise you to make sure the damaged nail is thoroughly clean to avoid infection by soaking it in a solution of salt water for 20 mins and allow to dry thoroughly. If you are unable to trim the loose extension without causing more trauma then leave it for now. When the nail is dry you can put a layer of petroleum jelly over it and then wrap it in a adhesive bandage to protect it. You need the wound to completely heal before any attempt to soak off in acetone, but if you are not trained I don't advise you to do this yourself, it should be done by a professional. If you feel at any point that your finger may have become infected you should see your GP.