Suppuration can occur from the periodontal pocket, with an oozing of pus around the gingival margin. If pus is able to escape through the periodontal pockets, then it's self-limiting, to a degree. But if the pus becomes less able to escape, or if there's another acute exacerbation of the periodontal pocket, this could lead to swelling, which could lead to an acute periodontal abscess (an acute suppurative inflammatory lesion within the periodontal pocket). So periodontal abscesses can occur as a result of progressive periodontitis.