Why do a second PhD in a "neighboring" discipline?

I've seen two reasons for this. The more worrisome reason is the one mentioned by EnergyNumbers in the comments, namely that some people just collect degrees. In particular, they may feel having two Ph.D.s would look exceptionally impressive, or they may be unable to settle on a specialization, or they may feel that getting another degree is somehow preferable to getting a job. These could be legitimate as personal desires, but they are counterproductive for a research career.

The other reason is to recover from a bad career start. Sometimes someone's grades keep them from getting into a good graduate program, or they face other constraints (geographical or financial) in their choice of programs, or they fail to connect well with their advisor. They may eventually get a Ph.D., but not under good circumstances, and a second Ph.D. might lead to a much better career. The difference between this case and the first case is that these students don't actually want a second Ph.D. as such. They regretfully feel they need one to achieve their career goals, but they wish it had been their first and only Ph.D.

Recovering from a bad start is a less worrisome reason to seek a second Ph.D., but of course the challenge is figuring out which students have moved beyond their past difficulties and which have not.

You didn't mention what country you are in or the relative standing of the two universities & supervisors involved. Sometimes people apply for a second PhD because their first one is not sufficiently well respected to get at good job.

Another reason is because the candidate really is just enjoying that stage of life. In the USA, one can often stay a PhD student for years in a top institution, but in other countries there are hard time limits. I also know of several people who took multiple PhDs at top universities just because they finished the first one too young to take a chair yet (and one person who didn't let that bother him & took a chair at 18, getting his father an office nearby!)

The most important question though is whether you want this person as a student – will they finish? Do they know what they are getting in to? If they have a PhD, they are in some sense a peer, and certainly should have a reputation. I would spend more time than usual pursuing the references, possibly with phone calls, and I would certainly talk at length with the candidate about whether they would really finish writing up a second time. I would only take them with exceptionally strong references from others and a very good personal narrative about why they want and would complete a second degree.

I think its all about the jobs that the first PhD could not bring to them. I myself have a PhD from an Egyptian university, but it seems that nobody is willing to offer me a post-doc position because I don't have 10 journal papers with extremely large impact factor as a PhD student from an advanced country would have. Of course the conditions are very different between a university in Egypt and another one in the United States or Europe. That's why I will keep looking for another PhD from a very high ranked western university.