Is there a way to recover the table wp_term_relationships?

I can’t offer you an explanation for what happened. But what I can unfortunately tell you is that you’ll have no luck on the WP side of things. There is no backup of that data.

I guess your best bet is still trying to save this MySQL table. Have you contacted the hosting provider? Maybe they have a backup.
Anyway you should ask this at some of the sister sites like https://dba.stackexchange.com/ or https://serverfault.com/ as they will be more able to help.

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