When discussing crossovers, keep in mind the term "crossover" isn't exactly accurate. In fact, each driver has a filter, or two, or three, between it and the amp.
A tweeter has a set of filters on it which typically do three things - three filters:
1) one to flatten out the hump in the impedance at the resonant frequency, a form of a notch filter centered onn the impedance resonance.
2) Another to reduce the voltage reaching the tweeter because most tweeters have a higher sensitivity than the rest of the drivers.
3) A high pass filter to limit the voltage reaching the tweeter below a certain frequency.
A midrange usually has two filters, but sometimes three or four:
1) One to limit the voltage above a certain frequency which is being handled by a tweeter.
2) Another to limit the voltage below a certain frequency which is being handled by a woofer.
3) Sometimes a third and forth to flatten the impedance curve to make those high pass and low pass filters work better.
A woofer will often have just one, but sometimes two or three filters:
1) One to limit the voltage above a certain frequency where the midrange (or tweeter) operate.
2) Sometimes an impedance leveler, and sometimes a shelf filter to compensate for the baffle step phenomenon.
A crossover is not one circuit, but a set of filters, each connected to one driver (or identical drivers in parallel) only to affect the voltage reaching each driver.
The description above is for a 3-way or 2-way "crossover".
In a 2.5-way crossover, as was already mentioned, one woofer will act as a mid/woofer and another will be a straight up woofer and not operate in the midrange. Both woofers operate below a certain frequency but only one of them operates up the frequency where the tweeter takes over.
This is accomplished by having three sets of filters:
Tweeter (same as above)
Mid/Woofer (same as above but for a two way speaker)
Woofer (same as above but for a three way speaker system).
In all cases, all of the filters are tuned to work together so the output of each driver compliments the output of the other drivers to get a combined performance as desired by the designer.
Now to the heart of the question that keeps coming up...
What frequency does the woofer driver have it's low pass filter tuned to?
It will vary depending on the needs of the design and goals of the designer.
For maximum output the woofer's crossover might be tuned to coincide with the frequency where the baffle step effect takes place. In other words, above a certain frequency the forward output of the mid/woofer is 6dB SPL louder because the full acoustic wave output is reflected forward versus below that frequency where the output is 6dB SPL quieter due to the acoustic wave wrapping around the cabinet. For a 12" wide speaker baffle, that frequency is around 300Hz. For a 8" wide baffle that frequency is about 425Hz. So, if the baffle is about 12" wide, the low pass filter for the woofer would be well suited to be around 300Hz, or so. For an 8" wide baffle the woofer's low pass filter would be suited to about 425Hz. The net result is a speaker where the output in the midrange sets the overall sensitivity of the entire speakers. Whereas, with a 2 way speaker the output SPL below the baffle step frequency will define the overall sensitivity of the speaker and shelving filter will have to be added to the mid/woofer to lower the output above the baffle step frequency to match the output in the bass.
Pros of this approach?
1) Higher sensitivity
2) Higher max SPL in the midrange and bass
3) Simpler mid/woofer crossover with fewer passive components to muck up the sound
Cons of this approach?
3) Not using a driver specific engineered for the range it operates in (the best speaker for 100Hz performance is not the best speaker for 1,000Hz performance).
4) Phase issues on the woofer's crossover impacting the clarity in the lower midrange or upper bass (depending on the frequency).
Another option is to use the woofer only to drive the deep bass output and extend the bass performance. With sealed speaker, specifically, placing a second woofer in a matching enclosure space below the mid/woofer and putting a low pass filter on it to operate below the -3dB point of the mid/woofer, the output could be extended by as much as 1 octave. So, if the -6dB bass extension with only a mid/woofer is 60Hz, the bass extension from adding a woofer below that point could be as low as 30Hz, though in reality a full octave of extension is almost never achieved.
Pros of this approach?
1) A surround sound system can be designed with larger mains with deeper output for lower bass management crossover settings.
2) Deeper output in pure stereo operation.
2) No real improvement in max SPL or sensitivity other than it can absorb twice the power in the deep, deep bass.
So, there you go.