if you're using DEA's i believe the container stays around on the DEA for
about an hour or so by default before being removed.

assuming you're on a DEA, to investigate, you'd need to know the DEA and
the warden handle to investigate, log in to the DEA as an operator with
bosh, then go the warden depot directory, find the warden handle and
execute bin/wsh from the container handle directory.

see:
http://docs.cloudfoundry.org/running/troubleshooting/troubleshooting-apps.html#access-warden

in diego, removing containers happens right away, but diego is also going
to support ssh for active troubleshooting and could just increase the
memory and attach jvm tools for debugging purposes to troubleshoot.

good luck.

--
Thank you,

James Bayer