Wrong question. The important question is: Will search engines recognize that this is content from a former site, now appearing on a new site, and if so, will they apply whatever penalties caused the now-defunct site to shut down in the first place?
Question #2: What happens to humans who used the old content? (If they didn't exist, there's not much point to reanimating the content anyway.)
Question #3, or possibly Question #0 before all others: Are both sites yours? Copyright doesn't vanish just because there is currently no physical representation of the copyrighted material.
If someone thinks that an old vanished site is worth preserving, they can create an online archive of it, for people who still want to see it.. Or even easier, just link to a copy at archive.org (the Wayback Machine)
New site without 301 redirect from old domain name (old site) is totally a new site and it has got nothing to do with whatever you were publishing on old site. Even if you have two similar sites without 301 they both will rank in Google search depending on multiple factors.