If, as Miss M states, that this offer is totally unacceptable to the BASSAnistas then there is the option for them to leave the airline and find another job with their requirements
This is a highly significant phenomenon and you should be congratulated for highlighting it. The strikers will be motivated to vote - in whichever way suits them, it is entirely possible some strikers will vote for acceptance. They will, though, form a high percentage of those who take part in the consultative ballot. What the opinion of the voters will be will be interesting.
Fatigue though will play a part, people weary of a constant struggle and some just want it to end. If BASSA do not actively campaign for refusal of the offer someone else will have to, else it is likely that support for continued action will melt away.