Hi,
we, www.a-kasser.dk is an online guide about A-kasse and Unemployment Benefits ("dagpenge"). We do not give advise about (other kinds of) social support/assistance, like for example "kontanthjælp", "integrationsydelse" and other social benefits that does not require membership of an Unemployment Insurance Fund ("A-kasse").
It is normally the "kommune" where you live, that you must contact about these other kinds of support.
if you don't meet the residency requirement, you are right...then you can not get Unemployment benefits.
People who don't meet the residence requirement, instead has the option to get Integration allowance/integrationsydelse. However this is meant for non-EU citizens. As an EU-citizen you can apply for social assistance ("kontanthjælp"), if you meet some conditions. You can find more information about social assistance in the following pdf-folder (p. 44):
https://a-kasser.dk/materiale/international/Your%20social%20security%20rights%20in%20Denmark_en.pdf
You apply for social assitance ("kontanthjælp") at the "kommune"-office in the town where you live.
Even though you are not qualified for Unemployment benefits, then I will suggest that you get you get your status changed from student to "graduate" in the A-kasse, on the day you finish your master. By this way you will have secured your "graduate rights" for the following two years. Could be relevant, If for example the residence requirement will be changed by a new government etc.
Let us know, if you have further questions.
Best regards,
Anders Weber, www.a-kasser.dk