There has been people who've been able to complete at least some of the dungeons solo (Kaeko soloed many on SCH), but for standard players and most jobs it's closer to impossible than possible. Group instances can't be entered without a party of 4/8 (if you try to enter with two people, Duty Finder will fill rest slots) but if some group members leave it's possible to continue with smaller group or alone (although it's likely to be very difficult depending on which roles you have).