In short answer, the plague did not leave at least from Europe entirely after this notorious outbreak, known as 'The Black Death', or 'The Great Mortality' by the contemporaries.
Some chroniclers as well as the fluctuation of testaments in Italian cities suggest that already in 1360s, Europe had a next wave of smaller scale of the outbreak. Spikes of this graph, assembled number of the testaments in six Italian cities (Fig. 12 in Cohn 2002: taken from Cohn 2002: 724), show a such tides of the outbreak continued into the 15th century at a short interval.
One scholar counts that the outbreaks of the plague still persisted almost every once in a decade (ca. 11.6 years) between ca. 1360 and 1500 (Aberth 2011: 37). While the mortality rate of the plague in respective outbreak seemed to decrease, it was likely that these recurrent waves of the plague hindered the rapid recovery of the population at least until the end of the Middle Ages (on contrary as a minority of scholars assume).
It was not until the 18th century that the middle to the large scale outbreak(s) of the bubonic plague almost entirely left from Europe: The last known large-scale outbreak in Western Europe occurred in ca. 1710 (in France).
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