Interest rate risk

Could there ever be a situation where. U have plain bonds and frns as assets. …fixed plain liabilities. …where rates go up…liabilities fall faster than assets …resulting in positive value ( 1% and 2% shift up) but at 3% and more…liabilities fall LESS than assets…making a negative value

Why would this happen?

Is it due to convexity ? The liabilities also have a greater maturity than assets