Furloughing is a new minefield for both employer and employees. Most employers made furlough choices on economic grounds, type of available work, and on any health/shielding requirements applicable to individuals. Data protection rules apply to other people's data so your employer would not necessarily be able to tell you full details of other employees/circumstances.
If it comes to a redundancy situation, the criteria for selecting posts must not discriminate directly or indirectly on any of the equality grounds such as gender, race, age or disability, and employers have to consider reasonable adaptions such as working from home for shielded disabled workers.
There is nothing preventing you from looking for alternative job while on furlough leave and handing in your notice in the normal way, but there are not many new opportunities elsewhere, and if you have long service with your current employer you will probably get some redundancy pay if the worst happens.
Another potential problem post redundancy if you become unemployed is the lack of a safety net, particularly if you do not have children at home ( or have savings) as universal credit, if you qualify, is unlikely to be enough to pay essential bills. It is best to prepare for the worst and hope it doesn't happen. You should be able to get job seekers allowance, which is a small non means tested taxable benefit based on your NI contributions, but there is a backlog of claims for that at the moment.