That happened to me a few times. All you need to do is keep contact with your client, is not your worry if he wants to keep the old hosting as long as he gives you the proper access, ftp, etc. You go on and develop the work and put it online, you don't have to deal with the web hoster.
The problem comes if you are afraid that the third person will somehow steal your software, because he will have access to that stuff, script and solutions that he can resell or use for his own projects without paying you.
You can still use your web hosting and tell to the other person to put your DNS in his configuration so you will not have this problem and your client will keep staying in the same hosting.
Also I take for granted that you will protect yourself with a contract and with proper pre-payments before publishing the final work.