Actually, it is impossible, as proven in the episode Chimera.
Well, it doesn't really contradict my reasoning above, since Laas is an extremely experienced shapeshifter and was not at all surprised by the Klingon's attack.
The changelings were never meant to be invulnerable and unkillable powerhouses. The writers state this explicitly, and the way they write Odo and the Founders for seven seasons makes this clear.
I think it's safe to say they would not have written a scene like Laas' fight with the Klingon in the early going, when they were concerned about Odo seeming too powerful. In season 7, this is no longer a concern.
One thing that is perfectly consistent throughout is the following: the changelings fear the solids and have been persecuted by them for eons
. How could this be if the changelings cannot be harmed by any conventional means?
From the beginning, we have been assuming in this thread that the two examples mentioned are oversights on the part of the writers, yet I doubt this is so. Their intention was simply for Odo to remain more or less on par with the other characters in terms of vulnerability.