Yeah, I've heard about image based programming, that enables editing your program as you run it. It scares the shit out of me.
See, if I have an unexpected error, that's because I fucked up my program. And because of that, my runtime state is likely screwed as well. So not only do I have to correct my error, I have to correct its consequences before I restart the program. I can't just resume its execution and hope for the best, I need to know that whatever state I keep is not rotten.
On the other hand, that way of doing things is not exclusive to dynamic languages. There's thing things called "dynamically loaded libraries", that you can use even in C. Game programmers routinely recompile & reload specific dlls just so they can correct their mistakes without restarting the whole game. And those who have written in-game editors have a very powerful stop-debug-restart cycle. On top of a statically typed language.