I meant more at the system/vm level. You're going to use a REPL (of some sort) for this, but the system needs to accommodate failure and just keep going, while giving you the opportunity to fix and change things.

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.