OK, at my place we would call this Leave of Absence (LOA). Generally the max of a year, or picking up where the student left off. Longer than a year could be tricky. Your DC will need strong documentation from a doctor./consultants who have been treating him/her. I hope your DC has been sensible about letting their department know that there are chronic health problems up to this point. A sudden request will be more difficult for the university to deal with -- or rather, your documentation will need to be very clear.
From a departmental view, at my place, we would look at our class registers, submitted assessment work etc, to estimate the last date of attendance. And we would sign a student off on LoA from that date. THat will be the date re funding (which I'm afraid I deliberately try to know nothing about as I need to be able to make academic judgements not swayed by considerations of finances).
In a full year course, it can be possible to pick up from where the student left off ie January next year. But think carefully about this: if there's been chronic ill-health, rather than a sudden crisis, it may be in the student's interests to redo the entire Final year from September 2013. In financial terms try if you can see it as an investment in the next stage of your DC's life -- getting a good degree class will make a difference.
From my POV as a tutor, I have been in the situation of urging tutees to take time out to get fully physically/mentally fit. University (particularly Final Year) is not the blag that most people think it is, and it can be tough on one's health. I think that t comes at a time in students' lives when there's sometimes a kind of 2nd adolescence, and a huge development spurt, and this can take its toll.
So it's good to hear that your DC is not going to jeopardise their final year (which is usually crucial for Degree classification) in a dogged attempt to cope when they're not coping.
To restart the course, we also require strong "Fit to study" certification. We try to get students to see that this is not a first aid band aid, but an attempt to get a more-or-less permanent solution to their fitness, rather than coping by limping on. It's tricky as so much self-worth can be tied up in a student's identity as a successful student. I find this especially the cae in mental ill-health situations. There, I use the analogy of a broken leg: if you're a skier and you break your leg, you take all the time out and all the therapy you can get to get fully fit and whole again; same with mental health. I know that's a reductive way to put it, but sometimes that can give students a useful and empowering perspective, rather than beating themselves up for being 'weak,' poor lambs.
Good luck and eventual good health!