Basically, you want to

1. get a line (or undef),
2. process the line, and
3. loop if appropriate,

in that order. The following snippets will do just that:

{
   local $_;
   do {
      $_ = <INHANDLE>;
      ...
   } while defined $_;
}
[download]

for (;;) { # Loop until "last".
   local $_ = <INHANDLE>;
   ...
   last if not defined $_;
}
[download]

{ # Loop while "redo".
   local $_ = <INHANDLE>;
   ...
   redo if defined $_;
}
[download]

my $block = sub { ... };
&$block while <INHANDLE>;
&$block foreach undef;
[download]

All of the snippets set $_ to undef on the last pass.

All of the snippets have access to the lexical variables, package variables and @_ of the parent scope.

Update: Moved local outside of the loop in first snippet.