I know that after I was made redundant and didn't claim benefits, I had all sorts of problems with my tax and took 2 years to get back tax overpayments. I basically had to prove to them that I was not receiving income and was instead living of my vast personal wealth (redundancy payment). I felt it not worth claiming benefits as the amount that I would have received (after working for 20 years) to support my husband and two small children didn't cover the amount that I usually spent on milk and yoghurts per week. My husband stayed at home to look after our children as his salary as a nurse was less after tax than the cost of childcare for two and we never claimed any benefits for the 5 years he was at home. It would be nice to think that there was help for us if we ever really needed it, but sadly, we are not used to living on such a small amount and don't have the knowledge of how to work the system that a lot of the long term claimants have, so I guess we are on our own.
However, I would point out that redundancy payments are meant to be spent in supporting yourself while you get another job, that's the reason that payment rates are higher as your age increases, they reflect that you may take longer to get a job when you are older, so therefore will need to support yourself for longer. In reality though, it is probably the biggest lump sum that most of us lay our hands on, so we like to salt it away as a nest egg rather than actually use it to live on - perfectly understandable, but not the purpose of the payment.