My recommendation: Absolutely nothing happens.
To see why, we need to look at the nature of the damage system in Dresden.
Stress, by itself, doesn't do anything. What causes you to be Taken Out is taking damage that you can't, or don't, soak with stress. (Consequences are only ever taken voluntarily, to avoid running out of stress. Admittedly this is usually on a "take one or die" basis, but it's still voluntary - you choose a consequence instead of taking some stress.)
And taking damage (or conceding if you're about to) is the only way to be taken out.
So - when the character transforms, the extra stress boxes go away. They're not in effect, ticked or otherwise. The stress in them doesn't go anywhere; it's out of play, just as the extra boxes are. The character can still soak stress normally with the boxes they have, and will take consequences (or lose) if those are exceeded as normal.
When they transform again, the extra boxes are back in play, just as they were.
At scene end, all boxes clear as normal, whatever form the character is in.
Another way to look at it is that stress represents exhaustion and energy used, not lasting effects. The human form has so much energy, which stops being available as it's used up (ticked). The tiger form has more, which also ceases to be available when ticked - or when not in tiger form. If it's not there, it doesn't really matter whether it's not there because you used it up already (ticked) or not there because you're in human form; what matters is that you can't use it to soak damage.
For another example of how this works, take a look at the closely related case discussed in this question.
It may seem tempting to impose consequences for "losing" the extra boxes, or move the stress down. Don't. The other form is intended to absorb damage that would kill the human form - that's what the power is for. If it can't safely do so, it's a little pointless. More importantly, this would also break an important Fate concept: that consequences are voluntary.
The only alternative plan would be: if a ticked stress-4 box goes away, that somehow reimposes the 4 stress, requiring (for example) a stress-2 tick and a mild consequence. I recommend against this in the strongest possible terms, as it has two serious flaws. Firstly, it neuters the power, since in the long run it won't protect against damage - just delay it. Secondly, it means you're GMing the combat damage retroactively, something that Fate does not benefit from, and tries hard to prevent.
(This is also consistent with the books - there are several occasions where we see members of Billy's gang seriously injured as wolves, then revert to human form when unconscious. Yet they don't suddenly die.)