Forwarding means "you really requested."
If it is not found, it is not found. Do not redirect.
Print a 404 status code, and then an HTML document that explains that everything requested was not found. Then you can offer to continue the journey, for example, by providing links to the main sections of the site or performing a search based on keywords extracted from the URL.
(The practical consequences of redirecting are that the URL disappears from the address bar, making it difficult to see the thought βOh, I saddened this letter, I just changed itβ or copy / paste it into the error report, etc.).
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