Crackling usually = Torn speaker. Can you see a tear, even small tear would cause it.
Only way you could damage a speaker is by wiring it incorrectly or clipping.
Audio signals are sinusoidal, when a audio signal clips it becomes closer to square, this causes the speaker to overheat, overexert itself, etc. and permanently damages it.
You can hear when the speakers clip tho, it'll be loud but really harsh. Usually clipping occurs when either the speaker cannot handle all the power the amplifier is outputting, therefore the speaker is moving outward or inward further than it is supposed to, or the amplifier isn't powerful enough.
The + and - on a speaker does matter btw. depending on the speaker type. Co-Axle, 6x9 and split systems all matter. Only a single mid range speaker with wired directly to the voice coils would not be affected. The reason is all those aforementioned speakers use capacitors or inductors to either cut out the high-range audio signals or low range audio signals. Wiring it incorrect will result in those signals no longer being filtered out and in case of certain capacitors it'll cause the capacitor to pop.
It is significant because if you don't filter the low range on a tweeter for example the tweeter will be damaged very quickly, it isn't meant to play low range audio. Mid range speakers can usually handle the high-range but it'll sound crap and put a damper on how loud the speaker can go before it'll clip. 6x9's, Co-axle and split system all include a mid-range and tweeter and the filters to filter mid/low-range and high-range. Cheaper speakers would only include low range filtering for the tweeter.
Most likely the crackling is caused by a torn/damaged tweeter