What determines whether slavery is economically efficient in industrialized/modern era economies?

Here's the crux:

That can't be right -- workers make enough to eat, profit their employers, plus buy comforts unavailable to slaves.

A worker works a number of hours for his boss, and get paid for those hours only. It varies amongst cultures and time periods, but usually when the worker gets sick or old, he has to take care of that himself - as well as for his family.

A slave has to be maintained 24/7. The employer has to provide food, shelter and medical care. Very often slaves were discarded when reaching old age. That wasn't a benefit. It was something slaves dreaded: if they could no longer work for their owners, they usually lacked the capability to fend for themselves.

In effect, a worker is like a machine. You pay mainly for operational costs. The maintenance costs are very low. Slaves are more like farm animals. The operational costs are low, but maintenance costs are very high.

As a whole debate sprang up, with a lot of downvotes, some clarication:

An employer pays for a certain job. Not because that employee is married and has children. That's a problem for the employee. And usually corrected on the free market. Few workers + lots of work = better conditions, and vice versa.

You can get paid more if you have more experience, or better qualifications. Not because you now have children, or decided to get married. In modern times you can get different tax rates or state benefits for having children/being married, but that is not controlled by the employer, therefore not relevant to the question.

Various different forms of slavery existed. From slaves condemned to mines up to ministers serving a royal. The first group was going to die within a year or two. The latter group would live very comfortably. Naturally, the first group weren't motivated to work hard. The latter group didn't need much motivation. Roman household slaves often got a bit of money, call a stipendium. Some slaves were able to save enough to buy their own freedom that way. But again, it wasn't the question.

I only address the bare bone basics. Which is that in general slaves are less productive than free labourers doing the same job. I've read somewhere even Cicero himself wrote a treatise in which he proved slavery wasn't economical. I can't recall the treatise, perhaps someone can put it in the comments?

Ancient unfree labor (in Roman times first largely foreign slaves and later domestic serfs) was "profitable" because wage labor was NOT the alternative. The alternative was the free peasant farm, which routinely underutilized its capital (land) to make the peasants as comfortable as they needed to be and no more. So a magnate with comparable land having slaves work it would extract more value.

Roman slavery in Sicily was vastly economically profitable. As was semi-slave relations in Roman Egypt, or slavery in Roman mines.

Unfree labour in capitalism has been profitable (but below the prevailing rate of profit) in the rum isles and cotton. Both of these industries had owned truck paid wage labourers who their bosses could kill. Cotton was profitable because it destroyed existing more complex markets and temporarily increased the over all rate of profit in the sector even though cotton growing was below rate. Rum similarly smashed British brewers and the drinking class was thereby forced into work.

Unfree labour in the Soviet Union and Germany was marginally loss making, and produced an overall social decline in gross product, but the cheap labour enabled GuLag and the labour camps to return an investment for their owners in marginal areas that would have been even worse if using free labour.

In these latter four capitalist examples bizarre social rituals reinforced slavery separate to its market returns: actual humans aren’t maximising marginalists.

In Rome value maximilalisation was not generalised.

The questions assumptions are wrong: market relations of wage labour are none of: ahistorical; universal; nor utterly determinant.