BillFitzmaurice.info

No, all what one can conclude from the melted plastic is that the crossover had too much power, and we know that the overheated inductor is the one in series with the woofer because it gets the most amount of current, so from that we can surmise a number of scenarios: tweeter cooked, woofer cooked or crossover damaged, that's why you have to run a frequency sweep to determine who is doing what.

We'd need to see the bottom of the board to tell you what the resistor is for. I'd guess it's a pad rather than protection.