... I am always missing the last digit of the process id ...
qr|$owner\s+(\d*)\w+...|
qr|$owner\s+(\w+)\w+...|

If your  $line is like the examples given by hippo and stevieb, the  \w+ immediately following the capturing  (\d*) (or following the  (\w+) in your Method 2) requires that the captured decimal sequence give back one digit in order to achieve an overall match. (Remember that  \w includes the  \d character class.)

c:\@Work\Perl\monks>perl -wMstrict -le
"my $line = 'ubuntu    9377  0.0  0.1  23668  1600 pts/2    S+   18:23
+   0:00 top';
 my $owner = 'ubuntu';
 ;;
 $line =~ m{ $owner \s+ (\d*) (\w+) }xms;
 print qq{captured:  (\\d*) ($1)  (\\w+) ($2)};
"
captured:  (\d*) (937)  (\w+) (7)
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The regex engine always does whatever is necessary to achieve an overall match.

Update: Oops... Didn't carefully read stevieb's post above, wherein all this is explained — and a bit better!