This has been implemented to varying degrees of reliability, granularity (in terms of preserving state) and utility. It's a common concept but I don't know the name for it!
Examples:
https://en.wikipedia.org/wiki/Continuation
https://en.wikipedia.org/wiki/Fault_tolerance
Maybe fault tolerance is the right word? But it doesn't imply that you actually modify and build the thing while it already runs.
An example of fail open design in the real world, is electronic magnetic locks at apartment complexes or business buildings. If the building loses power the doors demagnetize and unlock, then indefinitely remains open but failing because it is always open now. The opposite would be the building loses power and the doors fail close and lock the doors indefinitely when power is lost, and now people can’t escape.
a good read is ROC https://en.m.wikipedia.org/wiki/Recovery-oriented_computing
This is exactly what I do with the PyCharm - hit a breakpoint, write the code as it should be, and execute it in the debug REPL to do basic initial testing [repeat]. Extremely productive.
Yup, writing tests helps me sleep at night. TDD helps me manage my mental resources and iterate.
(another reason is communication--we code for our colleagues first, then for the machine: https://sonnet.io/posts/code-sober-debug-drunk/)
IIRC smalltalk had a workflow where you'd debug and write your program at the same time. You'd just reach a path that has not been implemented yet, break, implement it and continue.