There are some fibers coming out of my exhaust (looks like hair extensions!) I think it might be by

I was just wondering if anyone has any idea of how much this will set me back to get fixed and if the car is till safe to drive?

There are some fibers coming out of my exhaust (looks like hair extensions!) I think it might be by backbox...

Could be converter..but sounds more like muffler..the fiberglass packing in it has started to come apart it seems. Drive it...when it gets too loud have it fixed! Will be safe to drive as long as no external leaks.

There are some fibers coming out of my exhaust (looks like hair extensions!) I think it might be by backbox...

sounds like your catalyic converter is coming apart.

There are some fibers coming out of my exhaust (looks like hair extensions!) I think it might be by backbox...

Yep the fiberglass dampeners inside your muffler are coming out. Get a bendy stick and poke them back in there. The loose fibers won't do any harm. Maybe a bird/mouse climbed in there and started pulling them out to make a nest?

There are some fibers coming out of my exhaust (looks like hair extensions!) I think it might be by backbox...

From prior experience, this is coming from the internal components of the muffler or catalytic unit starting to deteriorate. If a good size glob beaks loose, it can block the breathing of the tail pipe system.

There are some fibers coming out of my exhaust (looks like hair extensions!) I think it might be by backbox...

As Bart says, most likely the internal baffles in your muffler are letting fibreglass out. Its not likely to cause any problems but may cause lower performance due to exhaust leaks.