In Tohoku, だ can follow verbs and い-adjectives, as I've heard (I've never actually spoken to someone from Tohoku). What purpose does it serve? Is a sentence ending in just a verb ungrammatical in Tohoku? And is this form used by Tohoku women?
In really rural, "pure" Tohoku dialect this is true. However, with the spread of Standard Japanese this is disappearing in young and working-age people. Even amongst the elderly it doesn't occur after everything, but it is common and grammatically correct within the dialect. This can also apply to "degasu" or "degozarusu", the Tohoku equivalent to "desu" or "degozaimasu", instead of taking the usual -ou ending to an -i adjective.
e.g. hayai > ohayou gozaimasu = ohayou gozarusu (because this is a set greeting) but [ii "de"gozaru(su)] instead of [you gozaru/gozaimasu]
Examples of this can be found in some of the example sentences on this website: https://konnok3.sakura.ne.jp/sendai01.html#sendai01