If one of the passengers has not reached airport yet, can the rest check-in while the remaining check-in later (to get their boarding pass)?
Each person is issued a separate ticket, you may all be on the same reservation, that is, have the same confirmation number but each passenger is given an individual ticket, even if they don't occupy a seat (as in the case of infants).
If you are all travelling on the same reservation number,
then you must check-in at the same time; otherwise the missing people are at risk of being classified as "no-show" which may have financial penalties depending on the type of ticket.
Apparently, there is no hard and fast rule on this (as per Zach's comment). I would call the airline and ask to be sure.
For me, I have yet to be in a situation where separate check-ins are allowed for the same reservation.