> Offering goods or services below the cost of their production is often illegal, though. It's called "dumping"

No.

Dumping is an international-trade term. It doesn’t even require pricing below cost, just aiming “to increase market share in a foreign market by driving out competition and thereby create a monopoly situation where the exporter will be able to unilaterally dictate price and quality of the product” [1].

Loss leaders are common in commerce and entirely legal, as are free trials. I struggle to think of a competent jurisdiction that bans them.

[1] https://en.wikipedia.org/wiki/Dumping_(pricing_policy)

I'm sorry, my fault. I studied economics in Russia, and the term "dumping" was used in a more general sense as "selling goods or services below their cost".

Russian laws officially use the term "monopolistically low prices", and prohibit them if the entity engaging in such pricing holds a dominating presence in the market (and not necessarily for the goods that are being underpriced).

A correct term for the US is "predatory pricing", and it's also prohibited by the Sherman Act. For much the same reason, a large entity can destroy competition by accepting losses from selling goods below the cost. The border between loss leaders and predatory pricing is, as usual, very blurred.