I agree completely with your latter statement on yielding - When a engineering plastic yields it stays elongated or stretched which also reduces it's cross section or diameter, permanently weakening the line, but in the first part of that paragraph, the yield strength or yield limit would be the point at which that permanent deformation occurred, not the point at which the line first started to stretch at all. The line will still stretch some up to that yield point, just not to the point/percentage of permanent deformation. This would be the elastic phase of the material. It's why if you're not careful, a bait suddenly pulled free from a snag might rocket right back at you like a projectile. That wouldn't happen without the elastic nature of the line. For example, braid won't do that (a nice thing)
If you take a length of nylon line (say 12# or 15# test to keep with the discussion) and measure that length, then add a 3# weight (or apply 3 pounds of pressure however you see fit), nylon line will stretch - a good 5-6% depending upon brand, and this would be immediate. As soon as you took the pressure off, the line would return to its original length since you didn't exceed the yield strength/limit. If you left the weight on, creep would eventually set in and that could become a permanent deformation even if you didn't exceed the yield point. In that regard, your point about leaving knots tied is a good one in this regard. Why risk possible deformation and weakness.
-T9