By 1970, the relationship started to give in (see the left-hand panel of the chart below). Even Milton Friedman came up with his own hypothesis on unemployment, which is the straight line Long Range Phillips Curve (LRPC), as seen in the above chart. By the subsequent decades, the relationship went haywire (see right-hand panel below). The Economist even devoted an article, "Heroes of the zeroes", whence I've sourced the charts in this post, on the Phillips curve.
Another way of presenting the relationship between inflation and unemployment is the Misery Index chart from Bloomberg (see below). Looked from this perspective, it is obvious that there's no relationship whatsoever between the two even as early as the 1920s and 1930s. Most economists are good at rationalising events which would have been easily disproved had they been more discerning with their observations.