I don't know how many times I've heard it...but it doesn't matter how many times...it's still wrong.
Putting a subwoofer in a smaller box does not increase power handling, it simply reduces efficiency and thus requires a larger amplifier. When designing a subwoofer especially one using equalization like a Bi-Quad (Linkwitz Transform) one of the primary considerations is the amplifier power required to drive the cone to it's maximum linear excursion. A bigger number here is a bad thing...not a good thing. The smaller the box, the bigger this number will be so you may want to look at the curve generated by your Linkwitz Transform software and think it is telling you that you have very high power handling but that's not what it's telling you. It's telling you that you have a very high power requirement...not power handling. It's probably telling you that the thermal limitation of the voice coil will be reached long before the excursion limitation. Contrary to popular belief, that's not a good thing. When I 'm designing a subwoofer I'm hoping that curve will tell me that 10 watts will drive the woofer to it's maximum excursion. Of course this is a very unrealistic expectation but it would be a very good thing if it were possible.
"I have +/- 25 mm linear excursion and I get it at 20 Hz with 10 watts"! Not... "I've got +/- 25 mm linear excursion and it would take 25,000 watts to exceed it at 20 Hz so I've got great power handling...I never have to worry about bottoming"! That second statement is just the wrong way to look at it folks! The less power required to bottom the woofer the better! That would be similar to reading a Fisher Investments on Materials report and thinking the way to get a higher investment return would be to start out buying high on some stock.
What your subwoofer can produce at any given low frequency is determined by one thing and one thing only. It is determined by how much air volume the woofer can displace. So, if my unrealistic subwoofer idea above were possible, it would get the most out of the woofer with just a 10 watt amplifier. If on the other hand someone has told you that you can increase your subwoofers power handling by putting it in a smaller box you will likely end up with a subwoofer that can no longer reach its full potential. With the smaller box, you have introduced a second limitation on what your woofer can produce, that is, the thermal limit of the voice coil.
A stiffer restoring force from the smaller box does not, "increase cone control". This is determined by the damping of the system. Qtc is Qtc...and this is what describes the control of the cone motion. Actually, decreasing the box size will increase Qtc and thus increase the chance of ringing...it will reduce cone motion control.
So, smaller box...more power required, possibly beyond the thermal limit...not more power handling. Also, smaller box...less control of cone not more control.
So if all the above is true how do we stop a woofer from bottoming? Well, we stop driving it in such a way as to bottom it! The question is, what is the woofer capable of based on its excursion limits. Once we know this, we can determine what HP filtering can resolve the problem. It could be that this woofer just can not produce 20 Hz at 115 db like you might want it to. That might require several times the excursion limit of the driver depending on what driver you are using. So, if you don't want it to bottom you just can't try to make it do something it can't do. Putting it in a smaller box isn't going to somehow magically enable it to do the 20 Hz at 115 db. The only viable solution is to use a HP filter. Just as with all speaker building this will be based on a balance of trade offs. If you want 20 Hz you will need to settle for less than the 115 db you hoped for or optionally you can keep your 115 db and settle for something higher than 20 Hz. You can't have both unless you get more or bigger woofers. No smaller box will change this. So, the solution is to use a HP filter to limit your woofer to a frequency range it can handle at the output level you desire. That's how you prevent bottoming, you don't put it in a smaller box and thus in a position such that it can never reach it's full potential.
Keep this one thought in mind, Infinite Baffle is better than sealed box. Infinite baffle has always been better than sealed box and it will always be better than sealed box. What is a smaller box doing? Moving farther away from infinite baffle! So, acoustically, a bigger sealed box is always better than a smaller one. The limitation should be based more on space limitations because making it smaller will never be a move toward optimization. Depending on the Q of the driver a very large box might move Qtc below the desired level but this can be corrected using the Linkwitz Transform. So the, "too big" box is still better assuming you correct the Q with a bi-quad. Of course a point of diminishing return can be reached with the box volume as the restoring force of the box becomes very small relative to that of the driver. At some point the large sealed box is essentially infinite baffle so making it bigger beyond this is not necessary.
As always, the above is my opinion. You have a right to your own opinion no matter how wrong your opinion might be;-)