It should be a cognate because the stems of the past subjunctive/Konjunktiv irrealis/II forms are the stems of the old preterite plural(and 2nd singular).
Compare the obsolete paradigm of sterben: ich starb, du stürbest, er starb, wir sturben, ihr sturbet, sie sturben. > the second stem + an originally different ending (causing the umlaut) lead to ich stürbe. The new paradigm became: ich starb, du starbst, er starb, wir starben... ich stürbe.
That's why the Konjunktiv forms are the same in every person and number.
Edit: as jknappen suggested, here's more about the two stems–
There used to be two stems for the preterite past of strong verbs differing in "ablaut" (a Proto-Indo-European vowel alternation further complicated by German(ic) sound changes)
sterben, starb, sturben.
In New High German [either the 1st or the 2nd stem] fell out of use and [one of the stems]. was used for every person and number. This lead to a clearer relationship of form and function, since the same tense and mood now had the same stem. But [when] the second stem [didn't survive in the indicative, it] sometimes survives in the Konjunktiv preterite mood with an Umlaut: stürbe.
Edit2 – Oh, I just remembered that it wasn't always the stem of 1./3.sg that was kept. For example reiten, ich reit, wir ri(t)ten. Here the second stem survived. In English and Scandinavian, though, the first stem survived rode, re(i)d.