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No. The tickets for the no-show passengers will be cancelled, but the rest of your party will be unaffected.
More specifically, the T&C for airlines (as a random example, here's Singapore Airlines) differentiate between a Ticket and the Passengers on that ticket. All the rules about showing up on time etc apply to individual Passengers, eg. Article 7:
If the Passenger fails to arrive in time at Carrier's check-in location or boarding gate [...] Carrier may cancel the space reserved for him.
Note the singular: the Passenger/him, not all Passengers/them.