Is it obligatory for a married person residing in a non-Muslim country, who is not working, to buy an Eid al-Adha sacrifice?

The Udhiyah (sacrifice) is a Sunnah, not an obligation. Therefore, there is no sin in not performing it, even if one is able, nor is one required to perform it if unable. This is because one of the conditions for it to be commanded is wealth, and jurists have differed in defining what constitutes the acceptable level of wealth.