The wire is what is loose not the cap. Well I think the wire is loose. The cap will have to be pried off I imagine. I've tried using a thin knife to pry it off, doesn't come off so easily, don't want to break it more.
OK Thats A Little Clearer, The Wire Is Pulling Off Inside Behind The Ash Cap.
I Don't Know What You Have For Tools, Time, Patients Or Skills But Heres Some Quick Options:
1) The Ash Cap Will Come Off But May Break & Be Careful. There Are Sometimes 2 Dimples On The Side Of The Plastic Cap To Use To Pry it Off, But It Is Extremely Brittle Plastic Usually, So It May Break, Once Off You Will See What To Do Or Not Do and Can Make A Decision On What You Are Willing To Do.
2) Easier: See If You Can Keep In A Working Position & Hot Glue, Epoxy, Crazy Glue It.
Hope That Helps
