Google's John Mueller responded on Twitter about if Google forgets about links over time, in which he responded "we have a lot of storage." That, to me, clearly means no. Google has said in the past that Google algorithms don't forget - here is John Mueller telling that to a webmaster yet another way.
Does Google forget about your old spammy links? Nope - they store that for a long long time according to this tweet.
Here is it:
@Rick_BarK @methode We have a lot of storage :).
— John ☆.o(≧▽≦)o.☆ (@JohnMu) May 3, 2017
Scary response, don't you think?
But of course, even if Google might not forget, they still may forgive - right? At least that has been Google's message with Penguin going real-time, disavow links tool, nofollow attribute, reconsideration requests and more.
So while Google doesn't forget - it seems they do forgive.
Forum discussion at Twitter.