View out of office responses from contacts
All the bounces, including the out-of-office responses, are saved. They're not accessible through civi, but for bounce processing you did have to configure an e-mail inbox somewhere. 

So just login in there and see what's available. E-mails in the main inbox folder are the unclassified ones (should be few — end up as Syntax error in the civimail report), while everything else will be in subfolders. There is no further division, so you can't just see out-of-office bounces, but not let's say, "quota full" or "invalid account". Wading through the mails can get annoying fast, even when searching with the server return codes.

However, I don't think you really need to do it. Looking at the bounce inbox is good now and then to see if any extra classification rules are needed (to reduce the unclassified mail amount) or if you're looking for the full email response for a particular contact (the database only stores a truncated version that may lack the server response), for example why it thought your e-mail was spam.

But all this bouncing around is tracked by civi. Contacts aren't disabled after one failed delivery; most of the rules require 3 such failures and then the "no bulk mail" setting gets enabled. The out-of-office one falls under the laxest of conditions, so last time I checked, it had to fail 15 times before a contact would be determined pointless to continue delivering to.

If your question instead is about people switching jobs, then yes, you'd have to look at the emails. Depending on where you are, you can't just subscribe random new people though (GDPR).