How to override exit() call in Perl eval block

exit isn't meant to be trapped, so eval isn't the solution here. You could put the remaining code you need to run in an END block:

some_function();
END { print "Still alive! For now...\n"; }

sub some_function {
    print "Hello from some_function\n";
    exit;
}

But if you absolutely, positively need to prevent exit from killing the script, you'll have to redefine exit() at compile time:

BEGIN { *CORE::GLOBAL::exit = sub (;$) { } } # Make exit() do nothing
some_function();
print "Still alive!\n"; # Gets printed

*CORE::GLOBAL::exit = *CORE::exit; # Restore exit()
exit;
print "I'm dead here.\n"; # Doesn't get printed

sub some_function { exit }

The Test::Trap module from the CPAN can be used to encapsulate this bit of ugliness for you, if you're interested in a more robust solution. Personally I would locally patch the exiting some_function() to use croak instead, and maybe file a bug report with the patch if it's a module.

If you're just evaling user input and you don't want them to be able to call exit, verify that the string contains no calls to exit or to a subroutine that would indirectly exit, then eval it. Personally I'd be more afraid of unlink and fork than exit if the user is inputting arbitrary code to be evaluated.

You can override exit, but you must do so at compile-time. So use a flag to signal whether the override is active or not.

our $override_exit = 0;
BEGIN { 
   *CORE::GLOBAL::exit = sub(;$) {
      CORE::exit( $_[0] // 0 ) if !$override_exit;

      die "EXIT_OVERRIDE\n";
   };
}

eval {
   local $override_exit = 1;
   some_function();
};

if ( !$@ ) {
   say "Normal return";
} elsif ( $@ eq "EXIT_OVERRIDE\n" ) {
   say "Exit called";
} else {
   print "Exception: $@";
}

But that creates an exception that might be caught unintentionally. So let's use last instead.

our $override_exit = 0;
BEGIN { 
   *CORE::GLOBAL::exit = sub(;$) {
      CORE::exit( $_[0] // 0 ) if !$override_exit;

      no warnings qw( exiting );
      last EXIT_OVERRIDE;
   };
}

my $exit_called = 1;
EXIT_OVERRIDE: {
   local $override_exit = 1;
   eval { some_function() };
   $exit_called = 0;
}

if ( $exit_called ) {
   say "Exit called";
} elsif ( $@ ) {
   print "Exception: $@";
} else {
   say "Normal return";
}

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Note that eval BLOCK is used to catch exceptions. eval EXPR is used to compile code.