If the neck relief changes, you still have to tune the string up to B, creating the same tension as before, unless I'm missing something here.
+1
Since the actual stiffness (deflexion) of a given type string is determined by the core wire, mass, gauge, length, and pitch, I am a bit skeptical of the sensation the OP is having that the string is less stiff (floppy). How would any of the aforementioned quantities vary without changing the string?
OK, mass might vary a tiny bit if the string wears or gets very dirty. If the core wire is seriously deformed by severe frets dents, that might affect it, too, though I am uncertain about that.
A change in setup, relief, etc. can't change the physics of tension, mass, pitch, mass, and core wire, IMHO.
What might change one's impression of stiffness? Here are my thoughts: you are tuning to the wrong pitch, you are becoming stronger in your plucking/slapping hand, you've changed the way your instrument is held, you are playing farther from the bridge, or you have been spending some time playing a different instrument--perhaps a four string or a 35" scale 5-string.
