Strong communication is the first component of properly managing redundancy. Preventing inaccurate information or gossip from spreading around the workplace is very important because otherwise such things can cause damage to a company in a variety of ways and make a difficult situation more difficult. Companies who run the communication, either written or verbal, by multiple relevant managers, executives, or HR representatives before it gets to the employee(s) being let go obviously do better than those who do not. Being open about the communication (not trying to hide anything), being clear/detailed to prevent confusion, and keeping records of all communication are also parts of strong communication regarding redundancy.
Supporting the employees being let go is the moral thing to do because such employees typically did not do anything wrong or have any issues with their performance. Companies will find it is also the cost-effective thing to do because employees who feel like they’ve been taken care of during the redundancy process are less likely to file a lawsuit against the company. Companies can support employees by offering them transfers to other (hopefully comparable) positions within the company, referrals to staffing agencies or other similar companies, or stipends designed to help with short-term financial issues.
All of the above is assuming the company has already attempted to prevent redundancies in the first place by taking annual inventory of the strategic goals of each business unit within the company or making the redundancies voluntary via buyouts or asking employees to retire early.