I'm sorry, I don't have a corrupt
pg_conversion table to help perform any verifications. My answers here must, by necessity, be heavily based on speculation.
With the limited information we have, I am guessing that you are attempting to do a full database
pg_dump, along the lines of
pg_dump --host 127.0.0.1 --port 5432 --username "postgres" ... "database_name"
If your data tables are still OK, you could try to
pg_dump the relevant schema(s)...
pg_dump --host 127.0.0.1 --port 5432 --username "postgres" ... --schema "schema_name" "database_name"
or table(s), and use multiple table switches...
pg_dump --host 127.0.0.1 --port 5432 --username "postgres" ... --table "table_name" "database_name"
With respect to these approaches, I have no idea if this will help, as I've simply never encountered a failing
pg_dump for any other reason than a syntax error, or something else relatively benign.
COPY to make CSVs
As a last ditch effort, if you aren't able to pg_dump your schema or tables, in a compressed
.backup format, you could always extract the data using the
COPY command to make comma-separated variable (CSV) files.
COPY table TO '/folder/table_backup.csv' WITH FORMAT CSV;
Good luck, and let us know if you have any success.