What does seem to happen often is that an owner who wants to move but doesn't want to lose their nice rate will move and then rent our their old place, or at least try to, it can be difficult to qualify for a new mortgage while carrying the old mortgage and not having a history of rent payments.
There's some exceptions, USDA, VA, and FHA loans. All government programs. But it's tied to the property so only transferable to the purchaser. Very rare here even now with rates changing so much.
ARM, 5/1 may be assumable depending on terms.
Typically people refix after the term. My 5 year recently ended and my monthly cost increased as I’m now fixed at a higher rate for another 5 years - at 4.5%, although it’s still less %age of my wage than it was 5 years ago.
During the fixed term you can’t repay it without a penalty, but if you move house you can port the mortgage so it’s secured against the new house instead.