Google's John Mueller has recently clarified when you need to disavow links and when you don't.
In a hangout on July 8th, Google's John Mueller said that you only need to disavow links that are really problematic. There is no need to disavow links simply because they are out of date or do not reflect that current state of your website.
The Google Disavow Links tool in the Search Console should only be used to disavow links that are spammy and completely problematic, stuff you just don't want associated with your website.
If your website changes over time and links become outdated or lead to 404 pages then there is absolutely no need to disavow them.
Google has an expectation thats sites evolve over time and links become outdated, so there is no need to disavow those links.
Here's the full extract from what Jonh Mueller said on the subject in disavowing links in response to a question about outdated product pages on a site as an example.
Disavowing backlinks is really mostly for the case where there are really problematic links pointing to your page and you want to say I want nothing to do with that. In a case like this, where these links might be completely normal links to your web site, they are just for older products or things you no longer provide, then that is something you don’t really disavow them for. Because this is something, that as a company, you kind of build up value over time, years… And it is normal that companies change their focus from time to time or shift their focus slightly.
So there you have it direct from Google. Only disavow problematic or spammy links that you don't want associated with your website. Outdated links as a result of website evolution can stay and may even benefit you in the long run.