On speakers built with properly designed L-Pads and crossovers, this is not a problem. In fact some of us actually model the various faults and what they may do to other components in the system.
There are some speakers that have been designed without thinking about the bigger picture... ie. we have this feature but you can't use it's full range without damaging something, or in the event of a failure of say a tweeter, some typed of power amps connected to the speaker might enter protect mode (hopefully) or blow up.
This is the difference between an engineered product and a product that's ok until it's not. (IMO) If the industry spent more time on the engineering and less time on the marketing, pretty pictures of sexy women holding basses they couldn't possibly play, and trying to be the cheapest product on the market, the misic community would probably be better off in the long run.
[rant off]
