Drivers fail from excessive power. With bass drivers it's a case of mechanical damage due to excessive excursion, together with overheating of the voice coil that can melt the glues that holds it together and/or the excessive heat distorts the coil former so the coil rubs against the magnet pole pieces.
Tweeters tend to burn out the voice coil, again from excessive power.
As to amplifier clipping, this generates higher levels of high frequencies due to distortion, and if this is combined with a higher powered amplifier, then the combination will burn out the tweeter. If it's a low powered amplifier that's being used, then even with clipping, it's unlikely that there will be enough HF energy to burn out the tweeter. Possible, but unlikely depending on the actual power of the amp and the rating of the tweeter. The worse possible combination is a highish powered amplifier overdriven to clipping, if the tweeter is a fairly fragile one.
It's mostly a myth that tweeters are burnt out more by a low power amp clipping than a high power amp. It depends on how much power, what tweeters, what type of programme material, i.e. how much HF there is in the music, It's excessive power that does for drivers, LF or HF.
One more benefit to active loudspeakers, drivers and amplifiers can be matched, and with DSP crossovers, HF limiters can act to protect the more fragile tweeters.
S.