They can delete the site at any time without notice.
Even so, saying the site is in no danger of closing, then suddenly closing it with no prior notice makes not only the CEO look like a liar, but also puts any brands he or she is managing at risk. Word of mouth travels fast and nothing is truly "erased" on the internet. Jumpstart would lose a lot of business and potential future customers for their other projects if people got wind of such things happening. And let me tell you, Neopets players are LOUD.
It is in JS's best interest to keep the site running if they say it's going to keep running. Even with the layoffs they are actively working to repair issues around the site, and if they were planning on closing things down, it would be a waste of time, resources, and brand integrity to do so.