Are over-discharged lithium cells safe? (And how to test for damage.)

This is one of the best Poundland purchases I've made in a while, purely because of the Google trek for knowledge that it sent me on. Most of Poundland's power banks in this style come completely discharged due to the higher than usual quiescent current of the circuitry. I wanted to know if that was a serious issue or not.

Here's the best documented test I found.
https://www.nature.com/articles/srep30248

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