If a program is ill-formed, a conforming implementation which has adequate resources to process it would be required to issue a diagnostic. Once an implementation has done so, anything it might do after that would be outside the Standard's jurisdiction. Some possible outcomes would be:
Terminate processing after outputting the diagnostic.
After outputting the diagnostic, proceed as though the language were extended to allow whatever constructs would otherwise make the program ill-formed.
Run the last successfully-compiled version of the program, whose behavior might bear no relationship to anything in the current source files.
If an construct is characterized as "Ill-formed; no diagnostic required", all of the above remain possible in addition to a fourth possibility, namely proceeding as though the language were extended to allow the construct without bothering to output a diagnostic first.
Since the Standard only seeks to describe program behavior in terms of the current contents of the source files, and not anything they might have contained at some time in the past, it cannot meaningfully describe might happen if an implementation is fed a ill-formed source file. That doesn't imply that quality implementations shouldn't seek to avoid accidental execution of obsolete versions of programs, but any measures they might take toward that end would be outside the Standard's jurisdiction.
Note that on some implementations that target embedded or remote systems, option #3 may not be nearly as absurd as it sounds. In many cases, a build-and-execute cycle would involve stopping execution on the remote system, feeding it new code, and then restarting execution on that system. If no new code image is available, restarting whatever code image was previously present may in many cases may be more useful than leaving the system in a dead state, but there's no way the Standard can impose anything meaningful about what that program does, implying that its execution as a consequence of the failure to build the new program cannot be characterized as anything other than Undefined Behavior.