Can an applicant's funding offer for PhD programs in the US be taken back and given to someone who's already declined it? This question pertains to math graduate programs in the US. Suppose a school sent a financial offer (TAship) to a student A and put a student B on the waitlist in the event that A declines the offer. Student A then declined the offer by signing the letter, so the school sent the offer to B. 

My question: is it possible that the school will rescind the offer from B if A changed his/her mind later on and decided the take the offer given that 

i) B has not yet accepted the offer.

ii) B has already accepted the offer.

iii) The date that A signed the letter to decline was before April 15th.
Note that your question is not really math-specific, but applies to essentially all programs at schools that have adopted the so-called April 15th resolution of the Council of Graduate Schools.

Once a student has turned down an offer of financial assistance and the offer has been given to someone else, it would be exceedingly poor form for a department to "claw back" the offer to give it to someone who has already declined the offer. If the student really wanted to attend—and the department still wanted the student—it could perhaps use a declined offer to get the student, but it couldn't take one that was "in the field" or already accepted to do so.

In general, the student has one chance to accept or decline. Student A could have waited until April 15 to decline the offer but decided to do so early. That decision is essentially irrevocable. It is also impossible for the school to rescind the offer to B once B has accepted, unless there exists cause to do so. (Examples where cause to withdraw a financial offer exists might include if student B fails to graduate or is shown to have made a fradulent application.)