Final answer:
As of December 31, 2000, the record for the most shutouts in the NHL was held by Terry Sawchuk with 103 shutouts, not by any of the options provided.
Step-by-step explanation:
The record for the most shutouts at the end of the 20th century, specifically on December 31, 2000, was held by Terry Sawchuk. Neither Patrick Roy, Martin Brodeur, Dominik Hasek, nor Ed Belfour held this record at that time. Terry Sawchuk set the long-standing record with 103 shutouts achieved during his career which spanned from 1949 to 1970. It is important to note that Martin Brodeur eventually surpassed this record during his career, but this occurred after the end of the 20th century. Brodeur played as a goaltender for the New Jersey Devils in the National Hockey League (NHL) and finished the 20th century with 105 shutouts, surpassing the previous record held by Terry Sawchuk.