Create a build script like the following:

<project name="failed-teardown" default="all"
         xmlns:au="antlib:org.apache.ant.antunit">
  <target name="all">
    <au:antunit>
      <file file="${ant.file}" />
      <au:plainlistener/>
    </au:antunit>
  </target>

  <target name="setUp">
    <echo>setUp</echo>
  </target>

  <target name="test1">
    <echo>test1</echo>
  </target>

  <target name="tearDown">
    <echo>tearDown</echo>
    <fail message="Failure in tearDown" />
  </target>
</project>

Running this test should result in a failed test run, but the test run succeeds
and the failure in tearDown is lost.