I think you are misunderstanding the phrase unpaid overtime in this context. Most jobs are salaried, not paid by an hourly rate, and small amounts of overtime required to get the job done do not get you extra money, but you cannot be forced to work more than 48 hours per week unless you specifically sign away your rights under the European working time directive.
As for insolvency law, if the a company goes under and has insufficient funds to cover outstanding wages then employees are entitled to up to £400 per week of outstanding pay, plus statutory redundancy rights (based on age and period of employment).
When a UK company enters administration then the appointed administrator replaces the directors.
Here is a question that probably betrays my naivety, but why can I even sign away my rights like that? What is to stop an employer from saying "We'll hire you, but only if you sign this, and if you don't we'll just find someone else." At that point, is it really a right? Or just a privilege afforded to those who aren't forced to sign it away?
The ability to opt out was very strongly backed by the UK government. I don't know if any other EU countries do it.
Although many companies ask you to opt out, they must not force you to do so. In addition an employee can opt in again with a certain amount of notice.
Depending on industry and country, unions are by-and-large very strong here in the EU, especially in Germany, and I wouldn't be surprised if they would very quickly put their foot down once such a practice becomes known.
As for insolvency law, if the a company goes under and has insufficient funds to cover outstanding wages then employees are entitled to up to £400 per week of outstanding pay, plus statutory redundancy rights (based on age and period of employment).
When a UK company enters administration then the appointed administrator replaces the directors.