HAve it pulled out. In fact, tie string round what's left of it and pull it out yourself. You won't notice if it's a back tooth, although chewing might be a little harder and you'll have to watch out for dry socket and so on.
There's not enough left to fill by the sound of it - so it will be a root canal and crown anyway - but if you leave it as it is you stand a good chance of getting an abscess which will bloody HURT like BLAZES and make you want to bang your head off the nearest hard object and you'll STILL need to go and have a root canal and so on (or have the tooth pulled out).
I lost one of my wisdom teeth after having DS1 - it just crumbled in my mouth, I only had 1/3 of the surface tooth left! 
Had it pulled out. No dry socket, no problem, just one less tooth to cause me bother in the future.
Get hypnotised by someone who's good at it before you go to the dentist, then they'll be able to do whatever's necessary. And sign a consent first before you pass out so that they can still carry on 
I do love your posts Honey - always entertaining!