Would I lose data if I change a column from varbinary(8000) to varbinary(max)? Is there any data loss if a table is being altered to change an existing column from varbinary(8000) to varbinary(MAX)?
No, you won't lose data.

SQL Server will do an in place conversion, as a transaction. This means if anything fails, it will rollback.

Note, this is more than a simple metadata change so it may take some time because data has to be moved around