Can a Graduate Student With Deficiencies Get an Assistantship for the Needed Undergraduate Courses?

I see many graduate program informational pages listed by various schools.

Many of them require specific undergraduate degrees, but also have discretionary exceptions for those without them. Most of them say something like:

"An applicant without satisfactory undergraduate training may be admitted to the program, but will be required to remove deficiencies by completing the necessary undergraduate courses without receiving graduate credit for them." - UND Physics & Astrophysics M.S.

I understand that the answer to this question is probably not all or nothing. Has anyone reading this had experience in such a situation or have any suggestions for a person seeking a graduate degree in any program with similar deficiencies who is strongly against debt and aims to make it through a program with an assistantship?

Is it typical for one who begins a degree with an assistantship to maintain it until program completion provided that they maintain satisfactory performance in all facets of the assistantship ie. academic and duty performance?