I have basically explained how to do it: keeping part of the previous chunk and appending the new chunk to it. The real difficulty is whether it is possible to determine the length of longest possible match for the regex (which determines how much to keep from one chunk to another). For some regexes, it is very easy, for others, it is very difficult or even impossible. The OP does not give enough information on that.
Then, there is the question of the size of the input. On my server, processing a 10 GB (line-based) file with a relatively simple regex might take 5 to 10 minutes. It would probably be a bit faster if not line-based, reading chunks of say 1 MB. With a TB of data, it would take quite a bit of time, but that might still be relatively manageable. But that's assuming a simple regex with no need to backtrack. With a regex implying a lot of backtracking, it might very easily be completely unmanageable.
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