European banks have cleared nearly half of the toxic loans off their balance sheets since emerging from a debilitating debt crisis earlier this decade. The only trouble: A chunk of those loans haven’t fully gone away.

Seen by some as a rare mark of progress in cleaning up Europe’s financial system, nonperforming loans sitting on banks’ balance sheets in the eurozone have fallen to 3.7% of the total, from 8% of total lending in 2014, according to the European Central Bank. In Italy, considered the epicenter of Europe’s banking problems, the figure is close to 8%, from a 17% peak.