Brian's answer surely hit a major part of the issue - the level of the UBI. Yet, there are other aspects of the problem.
- People like to work. There is a huge amount of sociological literature showing that people derive considerable non-pecuniary benefits from work, or alternative, that lack of work leads to several personal (and social) undesirables (for example, here, here, and here). As Voltaire said,
Work keeps at bay three great evils: boredom, vice, and need.
Thus, many people will like to work. This is the supply side of the labour market.
- Firms will still need workers. Provided capital and robots do not take over all jobs, firms will still require some workers. If the supply of labour across skill levels is not high enough, then either migration will occur (perhaps politically undesirable, but historically favoured by firms), or wages will go up. The latter will induce more people to work.
The key is, then, not only the level of UBI, but whether there will be enough jobs. Perhaps there will not be, at least not for the current working week. Maybe Keynes' prediction of a 15-hour working week might finally become true.