I'd be more worried about damaging your amp with a short in the crossover or something. I recall reading that a disconnected tweeter in a full crossover can cause issues with amps.
Jorg's setup might be high pass only though, in which case you're probably safe, I'd think.
Yep it'd be high-pass only for sure.
Damaging the amp is unlikely, not from a faulty attenuation circuit. But if the crossover is working at all, it means the series resistor is still connected so must be the parallel resistor that's fallen off. That means the crossover will still work, but the system impedance will be wrong, so the crossover will work at the wrong frequency. So what frequency is it working at now..... lets see.
Ok that resistor is most likely part of a 1.6dB attenuation circuit on an 8 ohm driver - not much attenuation there but hey, if it sounds good, it's right. Plus the variable L-pad is probably offering further attenuation because no-one ever runs them full up.
OK so if the parallel resistor is 47 Ohms, the series resistor must only be 1.6 ohms. So your 8 ohm circuit is now a 9.6 ohm circuit. that will only lower your crossover frequency by 500Hz or so (assuming 2nd order filter). If it was a 3.5k crossover before, it's currently operating at 3K now.
So you should be safe to keep using it. You're not in danger of blowing the horn, especially is you say you tend to turn it down anyway. But I'd still get it fixed because the effect of phase is unknown.
