Often the argument is made that automation = abundance which can resolve a lot of problems. However, this assumes that the abundance will be equally distributed, and that is not necessarily true in a capitalistic society (especially within the last decade with the top centile owning most of wealth and income). And if some of Piketty's arguments from Capital in the 21st century hold (particularly r > g), than wealth inequality will continue to increase.

However, inequality increasing itself is not a bad thing (in fact you need inequality for capitalism to work) if the overall quality of life for the bottom improves. If we can reach a point of diminishing marginal returns of just owning wealth (if it's true that people stop caring about collecting wealth once they have enough), than yes I think automation can help stop a collapse because working population won't care because they have enough wealth to be happy.

However, it is human tendency to base satisfaction and happiness RELATIVE to others (look at equity theory from management) so we may still end up in a situation where the quality of life for everyone has improved, but the working population still views that they're still inequal relative to the top (even though they're both better off) and we lead to instability. You can argue that has happened in our modern world today.