It's been awhile since I've taken introductory microeconomics. I remember increases in income move budget line outward. What if the increases have some condition?
Jill has $I$ to spend on food and clothing. One unit of food costs $p_F$ while one unit of clothing costs $p_C$.
Budget line is
Say Jill receives a $V voucher for food. What is the new budget line?
If the voucher was instead cash, we obviously have
If the voucher was really for food, we might not have $(*)$
However, I think we still have $(*)$ if:
$I > C' := (I+V)/p_C$ (the max that can be spent on clothing in $(*)$) because:
If the voucher is for food, then no more than $I$ is allowed to be spent on clothing.
However, such constraint is redundant if $I>C'$ because we know we won't exceed $C'$ and thus we won't exceed $I$.