Do IPs get "created" or are they all recycled?

When proxy services get "new" IPs, are they actually new or are they old ones that have been out of circulation for a while then put back into circulation.

Similarly, when a proxy service replaces an IP, what happens to the old IP?

Most services most likely receive used IPs from their datacenter and most proxy providers simply do have enough IPs. Due to cancellations they recycle their existing IPs.

But there is also the possibility to receive fresh IPs from ARIN.
Those are not "created" Ips are not a real product after all, but those were reserved until someone requires them.
In my case (seo-proxies.com) I still issue mostly fresh ARIN allocations, those have not been used before.

You should just ask the service you are interested in what they mean by "new".

This of course only counts for private proxy services that provide exclusive IPs hosted on datacenters.

Public proxies can also be "new", that just means that those IPs have been recently found or scraped.

Say an IP was blocked by Craigslist or any other website, can it be taken "offline" and refreshed somehow then be picked up by another company and be "unblocked" at a later date?

Do IP blocks just rest on the IP# or is it a combination of IP# and hosting company so if the hosting company changes, then the IP might lose it's block?

justone just gave you the correct answer. Just that there is more to proxies and IPs and countries. But the basic is covered by him

Let me try to provide answers with a different technique.

First, in today's world there's a shortage of IPs. When the internet first started I'm sure people couldn't imagine it would be so popular that would get ready to exhaust 256 x 256 x 256 x 256 IPs. (Things are now moving to IP6, using six classes instead of the existing four via IP4.)

Second, can an IP be somehow "refreshed?" In theory, yes. The Elbonian state government and internet provider might go bankrupt. So all the IPs for elbonia.gov and elbonia.net revert to ARIN (?) and can then be reissued to other providers. Or, as would be more likely, people buy the addresses direct from the Elbonians as they go bankrupt.

So, third: I would imagine that companies who bock certain IP addresses could remove the blocks after checking domain registrations and blocks of IP assignments when there was a real (as opposed to paper only) change in the providers to whom the IP addresses were assigned.

Fourth, absent this, I don't think there's much hope of getting a change made. If some company has blocked the IP addresses of spammers-r-us.com and they didn't make a mistake in doing so* my guess is that those IPs are going to stay blocked as long as the assignment doesn't change.

* In theory spammers-r-us.com could be a fan club for Hormel meat products (the people who make Spam). When they informed companies blocking their IP addresses of this the addresses would almost certainly be unblocked. Ditto for a company whose old net-abusing management got tossed out because of the net-abuse and the new incoming management set an entirely different policy.

Really, we can't wait for IPv6 - as it will be nearly impossible for these proxy detection scripts used by other companies (CBS, CL, etc.) to block them out (theoretically).