I'm not sure I understand your question 100%, but I think that what you are observing is a consequence of the fact that each line you type interactively in the debugger is in its own block/scope. Therefore, by using local you basically limit the change to $/ to that line. Watch: 

  DB<1> print "<$/>"
<
>
  DB<2> local $/

  DB<3> print "<$/>"
<
>
  DB<4> local $/; print "<$/>"
<>

[download]

Update: see also this node.

the lowliest monk

In reply to Re: confused about local $/ in perl debugger by tlm
in thread confused about local $/ in perl debugger by lupey

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