Does accumulated Zakat lapse, or does it remain a debt if one is unable to pay it, and is it permissible to take Zakat from parents to cover accumulated Zakat if their expenditure is not sufficient, even though it is obligatory upon them?

Zakat is a great obligation, and it is not permissible to be remiss in it or to delay it, except due to a lack of liquidity, with the necessity of striving to provide it. As for your taking from your parents' zakat, it has circumstances explained in previous fatwas. You should seek Allah's help and strive in your work to facilitate your affairs.