Any other political party may also nominate and file the required notice of a new candidate pursuant to § 24.2-539 if the candidate who died, withdrew, or had his nomination set aside was unopposed by that party. A nonparty candidate shall also be permitted to file a notice of candidacy whether or not the candidate who died, withdrew, or had his nomination set aside was opposed by a nonparty or party candidate. Any such party or nonparty candidate shall file any statement or petition required of him by Article 1 (§ 24.2-500 et seq.) or Article 2 (§ 24.2-505 et seq.) of this chapter.