[pcwalton]

Usually they either run debugged code in the interpreter or recompile the JIT code in a special instrumentation mode. (Not having to monkey patch the code at runtime—being able to do a "proper" recompilation—is one of the advantages of having a JIT!)

See this explanation of how it works in SpiderMonkey, for instance: http://rfrn.org/~shu/2014/11/20/speeding-up-debugger.html

[pjmlp]

Specially when coupled with the possibility to live connect to a production instance and do all sorts of monitoring and reports.

Of course, one needs to take care of the respective secure access. :)