Deferred admission but funding not guaranteed I received an offer from a top US school for PhD this March and accepted their offer. Due to some family circumstances, I would not be able to join the program this year. I am an international student, and I have to remain in my country due to some personal and family reasons.

I asked the program about possibility of deferring admission. After hearing my reason, they have decided to defer my admission, but I am not guaranteed funding. Basically, I need to compete with the next batch of applicants for funding (fellowship, TA, RA, or none). I agreed to the same, and I would be getting an offer sometime before April of next year along with funding allotment (if any).

In this context, my questions is: Can I apply to more programs to make sure I have a funded PhD offer for next year?

I realize that there is a certain commitment when deferring an offer, however does the same hold true even when funding is not guaranteed. When I asked the program about my chances of funding, they replied that it is "likely" but "not guaranteed". I am not sure if I can take a "likely" and live with that. What if I don't get any funding (which is basically a rejection) and don't have any other offers? That will be a very sad scenario. 

I would like some advice, IMO it is shrewd to apply to more programs, but is it ethical? I don't want to explicitly ask the program this question, since there is a likelihood that they may ask me to simply reapply, which I don't want to. I got off a wait-list, hence not very confident of my chances! Also, since funding is not guaranteed, do I even need to ask permission for applying to more programs? I mean, do they honestly expect a student to commit to a program without the program committing to financial support? I think that is asking a bit too much, and gives the program a complete hold over the student.

Also note that there is one other program (call Y) that I was admitted to this year, which I really liked. I had a very hard time choosing between the two offers, and had I not got into the program that I have accepted and deferred (call X), I would have gone to Y. I think I can get into Y again next year if I apply, since they tried hard to recruit me, but in the end I chose X because of better location (both were equally strong in research). So if X doesn't give me funding next year (effectively reject), I would like to go to Y.

Please share your thoughts. Thank you.
In brief, in academic mathematics, if you are "accepted" but without promise of funding, it's a very weak offer. The fact that you got funding this time around is certainly positive, but there's so much volatility involved that I think it would be a dangerous mistake to view the situation as so much promised to you (it's not) so that you have a complete obligation to go there and nowhere else. A promise of funding should be construed as obliging you to either keep your promise or decline in advance, but mere admission, without funding, while not nothing, is barely something, either.