There are 2 separate possibilities
First Oscar a retrenchment due to operational requirements and the second is changes to work conditions and terms, which may, to a certain extent related to operational requirements
Regarding refusing an offer, the offer must be reasonable, failing which the refusal does not exclude you from severance pay but the retrenchment may still be valid.
An offer of resignation indicates that the retrenchment was a fait complete and any consquotations would seemingly not be in good faith.
To return to the beginning, if operational requirements an restructuring is occurring there must be consultations with all effected people.
A change to terms and conditions aalso requires consultation.