Advisor dies suddenly, advice needed for research students
We had a similar situation at my university when a professor running a large group with millions of research dollars passed away. There are a few issues that have to be dealt with, and usually the department chair and/or the dean play a major role in this


research funding: often this can be transferred (in consultation with program managers) to faculty in related areas who (depending on the degree of involvement in the research) either merely manage the money for the students involved, or might play a more active role in spending it. 
students: students need committees and replacement advisors. Again, the department chair, in consultation with the students and related faculty, might be able to assign faculty as caretakers for the students. 
teaching/committees: while there are likely significant teaching/committee disruptions, these don't affect the former students of the researcher, so I'll ignore this component.


My view is that students that are close to graduating need someone who can sign off on their thesis work (hopefully without too much modification). They hopefully already have a few other people who can write letters for them for jobs, and can mention the advisor's demise in their letters to explain the absence. 

Students earlier in the Ph.D program (say just post-qualifying) are in the biggest bind: they've spent enough time in their research area to have committed to a topic, but now they have no one to guide them. They are the ones who probably need the most help from senior students, other faculty and the department. 

Students early in the program have the option of switching advisors, or even schools if there's no one else in the department who can advise them/fund them/works in their areas of interest. Again, the department is usually sympathetic and might be able to provide such students with short term funding via TAships if that's an issue. 

None of this of course addresses the feelings of grief and loss