A couple simple if hackish ways to handle this:

use 5.014;

$/ = \8192;
while (<>) {                    # like so
    state $buf .= $_ . ' 'x eof;
    $buf =~ s{ \s* (\S+) \s }{ process($1), "" }xge;
}
while (<>) {                    # ..or so
    state $buf .= $_ . ' 'x eof;
    $buf = pop( my $tok = [split ' ', $buf, -1] );
    process(@$tok);
}
sub process { say for @_ }
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The ' 'x eof may be omitted if \n endings are guaranteed.