You don't need the do if you don't use the value of the last expression. 
my $bigstring;
{ local $/; $bigstring = <FILE>; }

[download]

Update: Moreover, I tried both ways on a 2GB file and didn't notice any difference in memory consumption: 

  PID USER      PR  NI    VIRT    RES    SHR S  %CPU  %MEM     TIME+ C
+OMMAND
 7164 choroba   20   0 1970364 1.858g   3508 R 48.00 24.04   0:00.48 p
+erl
 7164 choroba   20   0 1970364 1.866g   3508 S 0.990 24.15   0:00.49 p
+erl
 7164 choroba   20   0 1970364 1.866g   3508 S 0.000 24.15   0:00.49 p
+erl
 7164 choroba   20   0 1970364 1.866g   3508 S 0.000 24.15   0:00.49 p
+erl
 7164 choroba   20   0 1970364 1.866g   3508 S 0.000 24.15   0:00.49 p
+erl

 7166 choroba   20   0 1970364 1.866g   3564 S 48.51 24.15   0:00.49 p
+erl
 7166 choroba   20   0 1970364 1.866g   3564 S 0.000 24.15   0:00.49 p
+erl
 7166 choroba   20   0 1970364 1.866g   3564 S 0.000 24.15   0:00.49 p
+erl
 7166 choroba   20   0 1970364 1.866g   3564 S 0.000 24.15   0:00.49 p
+erl
 7166 choroba   20   0 1970364 1.866g   3564 S 0.000 24.15   0:00.49 p
+erl

[download]

Code run: 

perl -wE 'my $string = do { local $/; <> }; say length $string; sleep 
+5' 2g
perl -wE 'my $string ; { local $/; $string = <> }; say length $string;
+ sleep 5' 2g

[download]

($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,

[download]

In reply to Re^4: memory use array vs ref to array by choroba
in thread memory use array vs ref to array by dkhosla1

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