Can I recover data from severely corrupted MS Access files?

My database file seems badly corrupted due to a system crash. Is it still possible to recover tables, queries, and indexes from such damaged MDB files?

You are aware to ask at a LibreOffice-site?
LO can only read tables via connectors (odbc, jdbc), if this connectors regognize the file/source as valid. There is no tool to debug damaged .mdb-files in LibreOffice. Queries in .mdb can only be used if they are stored as view and therefore show as tables.
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Generally: copy the current state, then search for your last working backup and try if you can open this. (Having no backup tells usually no valuable data expected, so no need to waste time …)
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For recovery check the tool of the manufacturer:

PS: I will change your tagging: Meta is something where this ask-site itself is the topic. (However - I had to include Base to remove meta…)