Somebody needs to explain this - as it makes no sense at all. PageRank is an arbitrary indicative measurement with next to no meaning, yet I see great domain names slipping by unsold, while ReallyLongCrapDomainWithYetMoreWords.net sells in hours just because it has PR*. Who is the person that is saying a PR'd domain gives any benefit at all? Please show the person so that we can disprove this myth; a myth which is costing a lot of poor people the very small amount of funds they have.
It really is true - domains that have PR and backlinks that were purchased with a backorder definitely have some extra power to them, compared to a brand new registered domain. After the domain dropped and was deleted from the registry, it's a different story though. The question of how valuable that extra power is though, is not easy to quantify
Recently expired/deleted domains may have the backlinks and good PR but not to old domain names. Google update the PR in a regular or irregular time interval, when the time of update if the site is functional then the page rank may be constant or some fluctuations occurs (depends on the quality of the backlinks), but if google found that site is not live, then the PR will be completely lost to that domain names. so check the PR of any domain name before purchasing that expired/deleted domain name. However, backlinks may be still available even though the site is not live.
I think having a PR does not mean that the domain is good directly because of its PR. In fact it should mean that the domain name has backlinks and that its probably an old name which also has value to Google. So, an old domain with backlinks definitely has some value for Google. If it's enough to pay a lot of money for it is another question and depends on the wanted price and the name itself.
PR's drop and rise at every update. If you're building an entire project just due to the PR of the domain, I wouldn't think thats the best thing to do