Actually it is impossible as web hosting will not use a fix IP, and the only reason of your case maybe your client domain has been blacklist, but not the IP.
I'm on a reseller web hosting package (Apache) on a shared server, and a client has complained that two contacts in the past day have complained to him of getting 'black listed' from our server. In other words, the senders (on third party servers) send him an email and they receive emails back from my server saying that the mail got rejected, 550-"JunkMail rejected". The mail-back also provides a spamcop.net URL for that IP to prove that it is blacklisted (and another contact was blacklisted on mxtoolbox.com). The strange thing is, one of these contacts could mail my client successfully yesterday, but later in the evening (yesterday) he sent a second email and it got rejected.
Is it possible that my shared-server could be reporting these IPs to third party servers, and they reject it? I'm asking my server support too, but I just want a second opinion on what is possible and what I should be aware of in terms of this.
How does an IP go on these blacklists anyway? I'm wary that my own server doesn't do that, but I'm curious if this is possible (e.g. shared hosting servers and generic web hosting providers in the USA - how can I know if they have the ability to report and add IPs to third party black lists?)