The trouble with 'relative poverty' is that the poorest 20% are always going to be the poorest 20%
Yes they will, but with a changed income distribution, they might not be in relative poverty any more. It's about feeling included in society.
The key thing is that it's a percentage of the median (the income of the middle person), not the mean (traditional average).
So, if you have:
1 person on 240k
2 people on 100k
6 people on 30k
1 person on 20k
Mean income is 60k
Median income is 30k
No-one is in relative poverty (60% of the median is 18k). There are enough people on 30k that the person on 20k will be able to afford the kind of things that are expected by society. Doesn't really matter that there are a few people with much more.
If instead you have:
1 person on 210k
7 people on 50k
2 people on 20k
Mean income is still 60k
Median income is 50k
The 2 people on 20k are now in relative poverty. The 'norm' is now to have 50k, which means that e.g all the other kids are going on a a school trip abroad, and the people on 20k risk feeling socially excluded.
It isn't about how rich the richest are (in both those cases, the median would stay the same if the super-rich guy moved abroad). It's about people not being left behind from the norm.