we do not guide about residence and work permit.
However for being eligible for dagpenge in case of unemployment, you must have a work and residence permit, that allows you to continue to stay in Denmark, and take any job with one day notice. So, a residence/work permit that are constrained to a specific job is not enough.
But in case you have the right residence/work permit, you can get dagpenge like all other individuals who meets the requirements.
It is out of the scope of our site to guide you about whether receiving dagpenge will affect your chances of achieving permanent residency. I think this is something you could ask SIRI about.
Let me know if you have further questions.
Anders Weber, www.a-kasser.dk