That depends on many factors I believe and mainly I would say on your new host's IP address, whether it is shared or dedicated IP and whether the IP has had past instances of abuse or bad activities so on so forth, and really you can't be guaranteed anything after a change of host, but for the most part you shouldn't be affected if you do the migration smoothly.
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Really it has nothing to do with the reputation of the host you are moving to (unless they are well known for hosting scammers/other bad web sites)
Basically what it comes down to is if they sold hosting to somebody on the IP that misused it in some bad way. An example would be that maybe somebody bought an account and spammed a bunch of people via email for about a day, it could get the mailserver IP blacklisted which would cause problems sending mail from that server. **This is an example, and probably wouldn't affect PR, but there are other things that could**
This is a big problem when it comes to shared hosting because if you have one bad apple on a server it can cause a lot of problems for everybody else. It's an inherant risk when you share a server with other people.
If you move the exactly site over and don't make too many changes for a while, you should be OK. However, DO NOT change the whois information on the domain during this time. I've seen sites go to a PR0 after moving hosts and new whois information which happened after a domain / site was sold.