Suppose a page is PR3 and gets deindexed for whatever reason (other than a penalty). And then it gets re-indexed while retaining all the backlinks it had from the start. Will it still be a PR3 after being re-indexed?
If you are meaning the little green toolbar PR, then my experience is that a site can fall out of the index for some time and still get it back. I have sometimes found though that it loses all PR or goes to lower.
If you're talking about a single page, then once that page is re-crawled and indexed it should eventually recover.
I don't know what happens if an entire domain is removed from the index. I would not be surprised if there are situations where Google might decide that a domain has changed ownership or gone through such a significant change that previous links are no longer counted - even if the domain registration does not change. I'd expect that the length of time involved would be a key factor in the process.