Advance parole is available only to those who have applied for adjustment of status and are not subject to the three or ten year bars to entry for having remained in the United States in "unlawful status" for more than 180 days (three year bar) or 12 months (ten year bar).
If an adjustment applicant was in lawful status at the time he or she filed for adjustment of status, the subsequent expiration of their nonimmigrant status is of no consequence. They remain in lawful status by virtue of having filed for adjustment of status while still in lawful status.
If an adjustment applicant was out of status at the time he or she filed for adjustment of status, the mere filing of the adjustment application will not prevent the accumulation of days in "unlawful status." To put it another way, if a person is "out of status" when they file for adjustment of status, they remain "out of status" (though not subject to removal) while their adjustment application is pending. The filing of the application does not stop the accumulation of time in "unlawful status." In such a case, if an adjustment applicant with more than 180 days in unlawful status were to go abroad, they would be prevented from re-entering the U.S. because the three year exclusion would apply.